test_values_test 23-Jun-2018 08:47:32 TEST_VALUES_TEST MATLAB version. Test the TEST_VALUES library. ABRAM0_VALUE_TEST: ABRAM0_VALUES stores values of the Abramowitz function of order 0. X FX 0.001953 0.8737772630698536 0.007812 0.8472185965045692 0.031250 0.7728893448398830 0.125000 0.5968434585345015 0.500000 0.2987173528367589 1.000000 0.1500459645051639 1.250000 0.1111466241915796 1.500000 0.0839095671531519 1.875000 0.0565523217179434 2.000000 0.0498764966030338 2.125000 0.0441008892197628 3.000000 0.0197385351802541 4.000000 0.0086193088287161 5.000000 0.0040224788162540 6.000000 0.0019718658458165 7.000000 0.0010045868340134 10.000000 0.0001572691726330 15.000000 0.0000103526669124 20.000000 0.0000009122975919 40.000000 0.0000000002562829 ABRAM1_VALUES_TEST: ABRAM1_VALUES stores values of the Abramowitz function of order 1. X FX 0.001953 0.4982821984879992 0.007812 0.4932439177304729 0.031250 0.4743161278469123 0.125000 0.4109598325876041 0.500000 0.2531761738822704 1.000000 0.1465633813859778 1.250000 0.1142154705601837 1.500000 0.0900263073834838 1.875000 0.0640882141707423 2.000000 0.0574466143141662 2.125000 0.0515816245648007 3.000000 0.0252637195557764 4.000000 0.0119308033301966 5.000000 0.0059270542280915 6.000000 0.0030609215358018 7.000000 0.0016307382136980 10.000000 0.0002837185191696 15.000000 0.0000211221501213 20.000000 0.0000020344578893 40.000000 0.0000000007111652 ABRAM2_VALUES_TEST: ABRAM2_VALUES stores values of the Abramowitz function of order 2. X FX 0.001953 0.4421385816210791 0.007812 0.4392337954568403 0.031250 0.4278985729709260 0.125000 0.3865282566185451 0.500000 0.2653820441323137 1.000000 0.1684873483833459 1.250000 0.1360920003251323 1.500000 0.1107033002772792 1.875000 0.0821260199955304 2.000000 0.0745387819995946 2.125000 0.0677320343776128 3.000000 0.0356418086988119 4.000000 0.0179565899566183 5.000000 0.0094058737143575 6.000000 0.0050809356204299 7.000000 0.0028149565414210 10.000000 0.0005380869642256 15.000000 0.0000448217563801 20.000000 0.0000046890678427 40.000000 0.0000000020161545 AGM_VALUE_TEST: AGM_VALUES stores values of the arithmetic geometric mean function. A B AGM(A,B) 22.000000 96.000000 52.2746411987042379 83.000000 56.000000 68.8365300598585179 42.000000 7.000000 20.6593011967340097 26.000000 11.000000 17.6968548737436500 4.000000 63.000000 23.8670497217533004 6.000000 45.000000 20.7170159828059930 40.000000 75.000000 56.1278422556166845 80.000000 0.000000 0.0000000000000000 90.000000 35.000000 59.2695650812296364 9.000000 1.000000 3.9362355036495553 53.000000 53.000000 53.0000000000000000 1.000000 2.000000 1.4567910310469068 1.000000 4.000000 2.2430285802876027 1.000000 8.000000 3.6157561775973628 AIRY_AI_VALUES_TEST: AIRY_AI_VALUES stores values of the Airy function Ai(x). X Ai(X) 0.000000 0.3550280538878172 0.100000 0.3292031299435381 0.200000 0.3037031542863820 0.300000 0.2788064819550049 0.400000 0.2547423542956763 0.500000 0.2316936064808335 0.600000 0.2098000616663795 0.700000 0.1891624003981501 0.800000 0.1698463174443649 0.900000 0.1518868036405444 1.000000 0.1352924163128814 AIRY_AI_INT_VALUES_TEST: AIRY_AI_INT_VALUES stores values of the integral of the Airy Ai function. X FX -12.000000 -0.7522883891661012 -11.000000 -0.5734835018585489 -10.000000 -0.7656984031342129 -9.500000 -0.6518101550538247 -9.000000 -0.5588197489447188 -6.500000 -0.5690235287071681 -4.000000 -0.4780074964292617 -1.000000 -0.4656739834670686 -0.250000 -0.0967831409456180 -0.000977 -0.0003468304985704 0.000977 0.0003465836691793 0.007812 0.0027657581846051 0.500000 0.1459533049118572 1.000000 0.2363173419171098 4.000000 0.3328926453861221 4.500000 0.3331875912977942 6.000000 0.3333294517052385 8.000000 0.3333333172424836 10.000000 0.3333333332991690 12.000000 0.3333333333332938 AIRY_AI_PRIME_VALUES_TEST: AIRY_AI_PRIME_VALUES stores values of the Airy function A'(X). X Ai'(X) 0.000000 -0.2588194037928068 0.100000 -0.2571304219075862 0.200000 -0.2524054702856195 0.300000 -0.2451463642190548 0.400000 -0.2358320344192082 0.500000 -0.2249105326646839 0.600000 -0.2127932593891585 0.700000 -0.1998511915822805 0.800000 -0.1864128638072717 0.900000 -0.1727638434616347 1.000000 -0.1591474412967932 AIRY_BI_VALUES_TEST: AIRY_BI_VALUES stores values of the Airy function Bi(X). X Bi(X) 0.000000 0.6149266274460007 0.100000 0.6598616901941892 0.200000 0.7054642029186612 0.300000 0.7524855850873156 0.400000 0.8017730000135972 0.500000 0.8542770431031556 0.600000 0.9110633416949405 0.700000 0.9733286558781659 0.800000 1.0424221712315609 0.900000 1.1198728131344471 1.000000 1.2074235949528711 AIRY_BI_INT_VALUES_TEST: AIRY_BI_INT_VALUES stores values of the integral of the Airy Bi function. X FX -12.000000 0.0176608190315546 -10.000000 -0.0150404248061400 -8.000000 0.0147564462932277 -7.500000 -0.1184730426484845 -7.000000 -0.0649167412661659 -6.500000 0.0972608324643810 -4.000000 0.0507600584952875 -1.000000 -0.3730050096342949 -0.250000 -0.1396298844266658 -0.001953 -0.0012001735266723 0.001953 0.0012018836117890 0.500000 0.3653384655095201 1.000000 0.8727691167380082 4.000000 48.2194752638034316 8.000000 440065.2580490417894907 8.500000 1760815.3976228302344680 9.000000 7377921.1705220006406307 10.000000 147809803.1074067056179047 12.000000 97037614223.6134338378906250 14.000000 116327376388098.7812500000000000 AIRY_BI_PRIME_VALUES_TEST: AIRY_BI_PRIME_VALUES stores values of the Airy function B'(X). X Bi'(X) 0.000000 0.4482883573538264 0.100000 0.4515126311496465 0.200000 0.4617892843621509 0.300000 0.4800490287524480 0.400000 0.5072816760506224 0.500000 0.5445725641405923 0.600000 0.5931444786342857 0.700000 0.6544059191721400 0.800000 0.7300069016152518 0.900000 0.8219038903072090 1.000000 0.9324359333927756 AIRY_CAI_VALUES_TEST: AIRY_CAI_VALUES stores values of the Airy function Ai(x) with complex argument. X Ai(X) 1.000000 0.000000 0.1352924163128814 0.0000000000000000 0.809017 0.587785 0.1433824486882056 -0.1092193342707378 0.309017 0.951057 0.2215404472324631 -0.2588711788891803 -0.309017 0.951057 0.4763929771766866 -0.3036484220291284 -0.809017 0.587785 0.5983692170633874 -0.0815460216077121 -1.000000 0.000000 0.5355608832923521 0.0000000000000000 -0.809017 -0.587785 0.5983692170633874 0.0815460216077121 -0.309017 -0.951057 0.4763929771766866 0.3036484220291284 0.309017 -0.951057 0.2215404472324631 0.2588711788891803 0.809017 -0.587785 0.1433824486882056 0.1092193342707378 AIRY_CBI_VALUES_TEST: AIRY_CBI_VALUES stores values of the Airy function Bi(x) with complex argument. X Bi(X) 1.000000 0.000000 1.2074235949528711 0.0000000000000000 0.809017 0.587785 0.9127160108293936 0.3800456133135556 0.309017 0.951057 0.6824453575635721 0.3343047153635002 -0.309017 0.951057 0.5726265660086474 0.3988641086982559 -0.809017 0.587785 0.2511841251049547 0.3401447690712719 -1.000000 0.000000 0.1039973894969446 0.0000000000000000 -0.809017 -0.587785 0.2511841251049547 -0.3401447690712719 -0.309017 -0.951057 0.5726265660086474 -0.3988641086982559 0.309017 -0.951057 0.6824453575635721 -0.3343047153635002 0.809017 -0.587785 0.9127160108293936 -0.3800456133135556 AIRY_GI_VALUES_TEST: AIRY_GI_VALUES stores values of the Airy Gi function. X FX -0.001953 0.2046830807004054 -0.125000 0.1837466283255790 -1.000000 -0.1166722172960153 -4.000000 0.3146693490272956 -8.000000 -0.3708904072242626 -8.250000 -0.2529305977242402 -9.000000 0.2896741065869270 -10.000000 -0.3464483649263409 -11.000000 0.2807603591387305 -13.000000 0.2181499450809486 0.001953 0.2052667900081050 0.125000 0.2212369536378477 1.000000 0.2352184398104379 4.000000 0.0828343033637687 7.000000 0.0457573854909893 7.250000 0.0441500120146052 8.000000 0.0399511337195089 9.000000 0.0354677068339497 10.000000 0.0318960051006796 12.000000 0.0265568927135124 AIRY_HI_VALUES_TEST: AIRY_HI_VALUES stores values of the Airy Hi function. X FX -0.001953 0.4093679827845889 -0.125000 0.3749529160804887 -1.000000 0.2206696067929599 -4.000000 0.0775653566797037 -8.000000 0.0396388264731247 -8.250000 0.0384500725750042 -9.000000 0.0352732168683179 -10.000000 0.0317685352825023 -11.000000 0.0288944082880514 -13.000000 0.0244632840116785 0.001953 0.4105354013999894 0.125000 0.4499350238120499 1.000000 0.9722051551424333 4.000000 83.7642371051043710 7.000000 80327.7449520447553368 7.250000 155141.3884774910693523 8.000000 1199585.9641733262687922 9.000000 21472868.8559676408767700 10.000000 455641153.5163291096687317 12.000000 329807225829.0476074218750000 ARCCOS_VALUES_TEST: ARCCOS_VALUES stores values of the arc cosine function. X FX -0.100000 1.6709637479564565 0.000000 1.5707963267948966 0.100000 1.4706289056333368 0.200000 1.3694384060045659 0.300000 1.2661036727794992 0.400000 1.1592794807274085 0.500000 1.0471975511965979 0.600000 0.9272952180016122 0.700000 0.7953988301841436 0.800000 0.6435011087932844 0.900000 0.4510268117962624 1.000000 0.0000000000000000 ARCCOSH_VALUES_TEST: ARCCOSH_VALUES stores values of the hyperbolic arc cosine function. X FX 1.000000 0 1.010000 0.1413037694856486 1.100000 0.4435682543851152 1.200000 0.6223625037147786 1.300000 0.7564329108569596 1.400000 0.8670147264905651 1.500000 0.9624236501192069 2.000000 1.316957896924817 3.000000 1.762747174039086 3.141593 1.811526272460853 4.000000 2.06343706889556 5.000000 2.292431669561178 10.000000 2.993222846126381 100.000000 5.298292365610485 1000.000000 7.600902209541989 ARCSIN_VALUES_TEST: ARCSIN_VALUES stores values of the arc sine function. X FX -0.100000 -0.1001674211615598 0.000000 0.0000000000000000 0.100000 0.1001674211615598 0.200000 0.2013579207903308 0.300000 0.3046926540153975 0.400000 0.4115168460674880 0.500000 0.5235987755982989 0.600000 0.6435011087932844 0.700000 0.7753974966107531 0.800000 0.9272952180016122 0.900000 1.1197695149986342 1.000000 1.5707963267948966 ARCSINH_VALUES_TEST: ARCSINH_VALUES stores values of the hyperbolic arc sine function. X FX -5.000000 -2.3124383412727525 -1.000000 -0.8813735870195430 0.000000 0.0000000000000000 0.100000 0.0998340788992076 0.200000 0.1986901103492414 0.300000 0.2956730475634224 0.400000 0.3900353197707153 0.500000 0.4812118250596035 0.600000 0.5688248987322475 0.700000 0.6526665660823557 0.800000 0.7326682560454109 0.900000 0.8088669356527824 1.000000 0.8813735870195430 2.000000 1.4436354751788103 3.000000 1.8184464592320668 4.000000 2.0947125472611012 5.000000 2.3124383412727525 10.000000 2.9982229502979698 100.000000 5.2983423656105888 1000.000000 7.6009027095419883 ARCTAN_VALUES_TEST: ARCTAN_VALUES stores values of the arc tangent function. X FX 0.000000 0.0000000000000000 0.250000 0.2449786631268641 0.333333 0.3217505543966422 0.500000 0.4636476090008061 1.000000 0.7853981633974483 2.000000 1.1071487177940904 3.000000 1.2490457723982544 4.000000 1.3258176636680326 5.000000 1.3734007669450159 10.000000 1.4711276743037347 20.000000 1.5208379310729538 ARCTAN_INT_VALUES_TEST: ARCTAN_INT_VALUES stores values of the Arctangent integral function. X FX 0.001953 0.0019531241721588 -0.003906 -0.0039062433772981 0.007812 0.0078124470192577 0.015625 0.0156245761819965 -0.031250 -0.0312466103494854 0.062500 0.0624729113350144 0.125000 0.1247841971738965 -0.250000 -0.2483017509823069 0.500000 0.4872223582945224 1.000000 0.9159655941772190 1.500000 1.2749694484943801 -2.000000 -1.5760154034463234 4.000000 2.4258878412859088 8.000000 3.3911633326292998 16.000000 4.4176450919422185 -20.000000 -4.7556713749547246 25.000000 5.0961912150934108 30.000000 5.3759175735714875 -50.000000 -6.1649904785027489 100.000000 7.2437843013083532 ARCTAN2_VALUES_TEST: ARCTAN2_VALUES stores values of the arc tangent function. X Y F 0.000000 -1.000000 -1.5707963267948966 0.500000 -0.866025 -1.0471975511965979 0.866025 -0.500000 -0.5235987755982989 1.000000 0.000000 0.0000000000000000 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.0471975511965979 0.000000 1.000000 1.5707963267948966 -0.500000 0.866025 2.0943951023931957 -0.866025 0.500000 2.6179938779914944 -1.000000 0.000000 3.1415926535897931 -0.866025 -0.500000 -2.6179938779914944 -0.500000 -0.866025 -2.0943951023931957 0.000000 -1.000000 -1.5707963267948966 0.500000 -0.866025 -1.0471975511965979 0.866025 -0.500000 -0.5235987755982989 1.000000 0.000000 0.0000000000000000 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.0471975511965979 0.000000 1.000000 1.5707963267948966 ARCTANH_VALUES_TEST: ARCTANH_VALUES stores values of the hyperbolic arc tangent function. X FX -0.500000 -0.5493061443340549 0.000000 0.0000000000000000 0.001000 0.0010000003333335 0.100000 0.1003353477310756 0.200000 0.2027325540540822 0.300000 0.3095196042031117 0.400000 0.4236489301936018 0.500000 0.5493061443340549 0.600000 0.6931471805599453 0.700000 0.8673005276940532 0.800000 1.0986122886681098 0.900000 1.4722194895832201 0.990000 2.6466524123622461 0.999000 3.8002011672501999 0.999999 7.2543286192620471 BEI0_VALUES_TEST: BEI0_VALUES stores values of the Kelvin function BEI of order 0. X FX 0.000000 0.0000000000000000 0.500000 0.0624932183821995 1.000000 0.2495660400366597 1.500000 0.5575600623030867 2.000000 0.9722916273066612 2.500000 1.4571820441598040 3.000000 1.9375867852660431 3.500000 2.2832499668539148 4.000000 2.2926903226993001 4.500000 1.6860172036321390 5.000000 0.1160343815502004 BEI1_VALUES_TEST: BEI1_VALUES stores values of the Kelvin function BEI of order 1. X FX 0.000000 0.0000000000000000 0.500000 0.1711951797170153 1.000000 0.3075566313755366 1.500000 0.3678649890020899 2.000000 0.2997754370020335 2.500000 0.0386684439659505 3.000000 -0.4874541770160708 3.500000 -1.3440423731111739 4.000000 -2.5638216885610778 4.500000 -4.1056854084008778 5.000000 -5.7979079017926249 BELL_VALUES_TEST: BELL_VALUES returns values of the Bell numbers. N BELL(N) 0 1 1 1 2 2 3 5 4 15 5 52 6 203 7 877 8 4140 9 21147 10 115975 BER0_VALUES_TEST: BER0_VALUES stores values of the Kelvin function BER of order 0. X FX 0.000000 1.0000000000000000 0.500000 0.9990234639908383 1.000000 0.9843817812130869 1.500000 0.9210721835462558 2.000000 0.7517341827138082 2.500000 0.3999684171295313 3.000000 -0.2213802495986939 3.500000 -1.1935981795899280 4.000000 -2.5634165572585799 4.500000 -4.2990865515997561 5.000000 -6.2300824786663576 BER1_VALUES_TEST: BER1_VALUES stores values of the Kelvin function BER of order 1. X FX 0.000000 0.0000000000000000 0.500000 -0.1822431237551121 1.000000 -0.3958682610197114 1.500000 -0.6648654179597691 2.000000 -0.9970776519264285 2.500000 -1.3730968976451110 3.000000 -1.7326442211284809 3.500000 -1.9596441312897490 4.000000 -1.8692484590318990 4.500000 -1.2028216314800859 5.000000 0.3597766667766728 BERNOULLI_NUMBER_VALUES_TEST: BERNOULLI_NUMBER_VALUES returns values of the Bernoulli numbers. N BERNOULLI(N) 0 1.0000000000000000 1 -0.5000000000000000 2 0.1666666666666667 3 0.0000000000000000 4 -0.0333333333333333 6 -0.0238095238095238 8 -0.0333333333333333 10 0.0757575757575757 20 -529.1242424242424249 30 601580873.9006423950195312 BERNOULLI_POLY_VALUES_TEST BERNOULLI_POLY_VALUES stores values of the Bernoulli polynomials. N X FX 0 0.200000 1.0000000000000000 1 0.200000 -0.3000000000000000 2 0.200000 0.0066666666666667 3 0.200000 0.0480000000000000 4 0.200000 -0.0077333333333333 5 0.200000 -0.0236800000000000 6 0.200000 0.0069135238095238 7 0.200000 0.0249088000000000 8 0.200000 -0.0101499733333333 9 0.200000 -0.0452782080000000 10 0.200000 0.0233263181575758 5 -0.500000 -0.3125000000000000 5 -0.400000 -0.1142400000000000 5 -0.300000 -0.0176800000000000 5 -0.200000 0.0156800000000000 5 -0.100000 0.0147400000000000 5 0.000000 0.0000000000000000 5 0.100000 -0.0152400000000000 5 0.200000 -0.0236800000000000 5 0.300000 -0.0228200000000000 5 0.400000 -0.0137600000000000 5 0.500000 0.0000000000000000 5 0.600000 0.0137600000000000 5 0.700000 0.0228200000000000 5 0.800000 0.0236800000000000 5 0.900000 0.0152400000000000 5 1.000000 0.0000000000000000 BERNSTEIN_POLY_01_VALUES_TEST: BERNSTEIN_POLY_01_VALUES returns values of the Bernstein polynomials. N K X BERNSTEIN(N,K)(X) 0 0 0.250000 1.0000000000000000 1 0 0.250000 0.7500000000000000 1 1 0.250000 0.2500000000000000 2 0 0.250000 0.5625000000000000 2 1 0.250000 0.3750000000000000 2 2 0.250000 0.0625000000000000 3 0 0.250000 0.4218750000000000 3 1 0.250000 0.4218750000000000 3 2 0.250000 0.1406250000000000 3 3 0.250000 0.0156250000000000 4 0 0.250000 0.3164062500000000 4 1 0.250000 0.4218750000000000 4 2 0.250000 0.2109375000000000 4 3 0.250000 0.0468750000000000 4 4 0.250000 0.0039062500000000 BESSEL_I0_VALUES_TEST: BESSEL_I0_VALUES stores values of the Bessel I0 function. X I0(X) 0.000000 1.0000000000000000 0.200000 1.0100250277951459 0.400000 1.0404017822293410 0.600000 1.0920453643173400 0.800000 1.1665149228698031 1.000000 1.2660658777520080 1.200000 1.3937255841340641 1.400000 1.5533950997312169 1.600000 1.7499806397389090 1.800000 1.9895593566180509 2.000000 2.2795853023360668 2.500000 3.2898391440501231 3.000000 4.8807925858650236 3.500000 7.3782034322254804 4.000000 11.3019219521363308 4.500000 17.4811718556092792 5.000000 27.2398718236044495 6.000000 67.2344069764779846 8.000000 427.5641157218047965 10.000000 2815.7166284662539510 BESSEL_I0_INT_VALUES_TEST: BESSEL_I0_INT_VALUES stores values of the integral of the Bessel function I0. X FX 0.001953 0.0019531256208818 -0.003906 -0.0039062549670566 0.062500 0.0625203480325466 0.125000 0.1251628558136697 -0.500000 -0.5105148087974031 1.000000 1.0865210970235899 2.000000 2.7750019054282533 -4.000000 -13.7752088680397158 8.000000 464.2437205810610976 18.000000 6411186.7658021580427885 -18.500000 -10414860.8031758572906256 20.000000 44758598.9138557463884354 -21.000000 -118529853.1155828833580017 22.000000 314300782.2071599364280701 -23.000000 -834402129.0079431533813477 24.000000 2217536757.9074296951293945 25.000000 5899173184.2803640365600586 -27.000000 -41857073244.6915206909179688 30.000000 795538858184.7236328125000000 40.000000 15089715082719202.0000000000000000 BESSEL_I0_SPHERICAL_VALUES_TEST: BESSEL_I0_SPHERICAL_VALUES stores values of the i0 spherical Bessel function. X FX 0.100000 1.0016675001984401 0.200000 1.0066800127054700 0.400000 1.0268808145070389 0.600000 1.0610893035804021 0.800000 1.1101324777345289 1.000000 1.1752011936438009 1.200000 1.2578844628434771 1.400000 1.3602153581796670 1.600000 1.4847299707501440 1.800000 1.6345412711642671 2.000000 1.8134302039235091 2.200000 2.0259568956981329 2.400000 2.2775955056983732 2.600000 2.5748970109206448 2.800000 2.9256851265128270 3.000000 3.3392916424699668 3.200000 3.8268387489267162 3.400000 4.4015774672701014 3.600000 5.0792931557264849 3.800000 5.8787912791374550 4.000000 6.8224792992819383 BESSEL_I1_VALUES_TEST: BESSEL_I1_VALUES stores values of the Bessel I1 function. X I1(X) 0.000000 0.0000000000000000 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.000000 0.5651591039924850 1.200000 0.7146779415526431 1.400000 0.8860919814143274 1.600000 1.0848106351298801 1.800000 1.3171672303918991 2.000000 1.5906368546373291 2.500000 2.5167162452886980 3.000000 3.9533702174026089 3.500000 6.2058349222583651 4.000000 9.7594651537044506 4.500000 15.3892227537359201 5.000000 24.3356421424505314 6.000000 61.3419367776402424 8.000000 399.8731367825600955 10.000000 2670.9883037012550631 BESSEL_I1_SPHERICAL_VALUES_TEST: BESSEL_I1_SPHERICAL_VALUES stores values of the i1 spherical Bessel function. X FX 0.100000 0.0333666785736334 0.200000 0.0669337145680295 0.400000 0.1354788933285401 0.600000 0.2072931911031093 0.800000 0.2841280857128948 1.000000 0.3678794411714423 1.200000 0.4606425870674146 1.400000 0.5647736480096238 1.600000 0.6829590627779635 1.800000 0.8182955028627777 2.000000 0.9743827435800611 2.200000 1.1554324696364060 2.400000 1.3663965255279731 2.600000 1.6131187675720640 2.800000 1.9025154608386809 3.000000 2.2427901177692662 3.200000 2.6436898286303570 3.400000 3.1168115268848728 3.600000 3.6759683131489318 3.800000 4.3376279877476422 4.000000 5.1214383841836373 BESSEL_IN_VALUES_TEST: BESSEL_IN_VALUES stores values of the Bessel In function. N X IN(X) 2 0.200000 5.0166875138946783e-03 2 1.000000 1.3574766976703831e-01 2 2.000000 6.8894844769873820e-01 2 2.500000 1.2764661478191639e+00 2 3.000000 2.2452124409299512e+00 2 5.000000 1.7505614966624240e+01 2 10.000000 2.2815189677260041e+03 2 20.000000 3.9312785221040763e+07 3 1.000000 2.2168424924331898e-02 3 2.000000 2.1273995923985270e-01 3 5.000000 1.0331150169151140e+01 3 10.000000 1.7583807166108529e+03 3 50.000000 2.6777641388839410e+20 5 1.000000 2.7146315595697189e-04 5 2.000000 9.8256793231317023e-03 5 5.000000 2.1579745473225458e+00 5 10.000000 7.7718828640326001e+02 5 50.000000 2.2785483079112819e+20 10 1.000000 2.7529480398368742e-10 10 2.000000 3.0169638793506839e-07 10 5.000000 4.5800444191760508e-03 10 10.000000 2.1891706163723370e+01 10 50.000000 1.0715971594776370e+20 20 1.000000 3.9668359858190202e-25 20 2.000000 4.3105605761095479e-19 20 5.000000 5.0242393579718059e-11 20 10.000000 1.2507997356449481e-04 20 50.000000 5.4420084027529984e+18 BESSEL_IX_VALUES_TEST: BESSEL_IX_VALUES stores values of the Bessel In function for NONINTEGER order. N X IN(X) 0.500000 0.200000 3.5920841758336142e-01 0.500000 1.000000 9.3767488824548761e-01 0.500000 2.000000 2.0462368630890548e+00 0.500000 2.500000 3.0530935381967179e+00 0.500000 3.000000 4.6148229034076014e+00 0.500000 5.000000 2.6477547497559069e+01 0.500000 10.000000 2.7787846038745711e+03 0.500000 20.000000 4.3279746272428930e+07 1.500000 1.000000 2.9352532634747980e-01 1.500000 2.000000 1.0994731886331099e+00 1.500000 5.000000 2.1184442264794139e+01 1.500000 10.000000 2.5009061549421181e+03 1.500000 50.000000 2.8666537159314640e+20 2.500000 1.000000 5.7098909203048248e-02 2.500000 2.000000 3.9702708013939048e-01 2.500000 5.000000 1.3766882138682581e+01 2.500000 10.000000 2.0285127573919360e+03 2.500000 50.000000 2.7531576300354021e+20 1.250000 1.000000 4.1394160156423521e-01 1.250000 2.000000 1.3401967589828969e+00 1.250000 5.000000 2.2857155103646701e+01 1.250000 10.000000 2.5930067634320021e+03 1.250000 50.000000 2.8866300750777660e+20 2.750000 1.000000 3.5909104832510821e-02 2.750000 2.000000 2.9311086362664829e-01 2.750000 5.000000 1.1993970100230680e+01 2.750000 10.000000 1.8945757315623830e+03 2.750000 50.000000 2.7169113757604830e+20 BESSEL_J_SPHERICAL_VALUES_TEST: BESSEL_J_SPHERICAL_VALUES stores values of the j spherical Bessel function. N X FX 0 0.905000 0.8689780717709105 1 0.905000 0.2776712616989048 2 0.905000 0.0514791493304315 3 0.905000 0.0067439279719875 4 0.905000 0.0006838294584220 5 0.905000 0.0000565859791709 6 0.905000 0.0000039559237659 7 0.905000 0.0000002394450911 8 0.905000 0.0000000127794011 9 0.905000 0.0000000006099572 10 0.905000 0.0000000000263310 0 10.000000 -0.0544021110889370 1 10.000000 0.0784669417987515 2 10.000000 0.0779421936285624 3 10.000000 -0.0394958449844703 4 10.000000 -0.1055892851176917 5 10.000000 -0.0555345116214522 6 10.000000 0.0445013223340943 7 10.000000 0.1133862306557747 8 10.000000 0.1255780236495678 9 10.000000 0.1000964095484906 10 10.000000 0.0646051544925643 BESSEL_J0_VALUES_TEST: BESSEL_J0_VALUES stores values of the Bessel J0 function. X J0(X) -5.000000 -0.1775967713143383 -4.000000 -0.3971498098638474 -3.000000 -0.2600519549019334 -2.000000 0.2238907791412357 -1.000000 0.7651976865579666 0.000000 1.0000000000000000 1.000000 0.7651976865579666 2.000000 0.2238907791412357 3.000000 -0.2600519549019334 4.000000 -0.3971498098638474 5.000000 -0.1775967713143383 6.000000 0.1506452572509969 7.000000 0.3000792705195556 8.000000 0.1716508071375539 9.000000 -0.0903336111828761 10.000000 -0.2459357644513483 11.000000 -0.1711903004071961 12.000000 0.0476893107968335 13.000000 0.2069261023770678 14.000000 0.1710734761104587 15.000000 -0.0142244728267808 BESSEL_J0_INT_VALUES_TEST: BESSEL_J0_INT_VALUES stores values of the integral of the Bessel function J0. X FX 0.000977 0.0009765624223898 0.003906 0.0039062450329491 -0.062500 -0.0624796579279179 0.125000 0.1248373349212048 -0.500000 -0.4896805066460451 1.000000 0.9197304100897602 -2.000000 -1.4257702931970266 4.000000 1.0247341594606065 -8.000000 -1.2107468348304502 16.000000 1.1008652032736190 -16.500000 -1.0060334829904125 18.000000 0.8133057266248596 -20.000000 -1.0583788214211278 25.000000 0.8710149211654588 -30.000000 -0.8842490888254749 40.000000 1.1257761503599915 -50.000000 -0.9014121225818346 75.000000 0.9144134436964779 -80.000000 -0.9448228193833440 100.000000 0.9226625569601661 BESSEL_J0_SPHERICAL_VALUES_TEST: BESSEL_J0_SPHERICAL_VALUES stores values of the j0 spherical Bessel function. X FX 0.100000 0.9983341664682815 0.200000 0.9933466539753061 0.400000 0.9735458557716262 0.600000 0.9410707889917256 0.800000 0.8966951136244035 1.000000 0.8414709848078965 1.200000 0.7766992383060221 1.400000 0.7038926642774715 1.600000 0.6247335019009407 1.800000 0.5410264615989973 2.000000 0.4546487134128408 2.200000 0.3674983653725410 2.400000 0.2814429918963129 2.600000 0.1982697583928709 2.800000 0.1196386250556803 3.000000 0.0470400026866224 3.200000 -0.0182419198211187 3.400000 -0.0751591476549504 3.600000 -0.1229223453596812 3.800000 -0.1610152344586103 4.000000 -0.1892006238269821 BESSEL_J0_ZERO_VALUES_TEST: BESSEL_J0_ZERO_VALUES stores zeros of the Bessel J0 function. K X(K) 1 2.404825557695773 2 5.520078110286311 3 8.653727912911013 4 11.79153443901428 5 14.93091770848779 6 18.07106396791092 7 21.21163662987926 8 24.3524715307493 9 27.49347913204025 10 30.63460646843198 11 33.77582021357357 12 36.91709835366404 13 40.05842576462824 14 43.19979171317673 15 46.34118837166181 16 49.48260989739781 17 52.624051841115 18 55.76551075501998 19 58.90698392608094 20 62.04846919022717 21 65.18996480020687 22 68.3314693298568 23 71.47298160359374 24 74.61450064370183 25 77.75602563038805 26 80.89755587113763 27 84.0390907769382 28 87.18062984364116 29 90.32217263721049 30 93.46371878194478 BESSEL_J1_VALUES_TEST: BESSEL_J1_VALUES stores values of the Bessel J1 function. X J1(X) -5.000000 0.3275791375914652 -4.000000 0.0660433280235491 -3.000000 -0.3390589585259365 -2.000000 -0.5767248077568734 -1.000000 -0.4400505857449335 0.000000 0.0000000000000000 1.000000 0.4400505857449335 2.000000 0.5767248077568734 3.000000 0.3390589585259365 4.000000 -0.0660433280235491 5.000000 -0.3275791375914652 6.000000 -0.2766838581275656 7.000000 -0.0046828234823458 8.000000 0.2346363468539146 9.000000 0.2453117865733253 10.000000 0.0434727461688614 11.000000 -0.1767852989567215 12.000000 -0.2234471044906276 13.000000 -0.0703180521217784 14.000000 0.1333751546987933 15.000000 0.2051040386135228 BESSEL_J1_SPHERICAL_VALUES_TEST: BESSEL_J1_SPHERICAL_VALUES stores values of the j1 spherical Bessel function. X FX 0.100000 0.0333000119025576 0.200000 0.0664003806703222 0.400000 0.1312121544218529 0.600000 0.1928919568034122 0.800000 0.2499855053465475 1.000000 0.3011686789397568 1.200000 0.3452845698577903 1.400000 0.3813753724123076 1.600000 0.4087081401263934 1.800000 0.4267936423844913 2.000000 0.4353977749799916 2.200000 0.4345452193763121 2.400000 0.4245152947656493 2.600000 0.4058301968314685 2.800000 0.3792360591872637 3.000000 0.3456774997623560 3.200000 0.3062665174917607 3.400000 0.2622467779189737 3.600000 0.2149544641595738 3.800000 0.1657769677515280 4.000000 0.1161107492591575 BESSEL_JN_VALUES_TEST: BESSEL_JN_VALUES stores values of the Bessel Jn function. N X JN(X) 2 1.000000 0.1149034849319005 2 2.000000 0.3528340286156377 2 5.000000 0.0465651162777522 2 10.000000 0.2546303136851206 2 50.000000 -0.0597128007942588 5 1.000000 0.0002497577302112 5 2.000000 0.0070396297558717 5 5.000000 0.2611405461201701 5 10.000000 -0.2340615281867936 5 50.000000 -0.0814002476965696 10 1.000000 0.0000000002630615 10 2.000000 0.0000002515386283 10 5.000000 0.0014678026473105 10 10.000000 0.2074861066333589 10 50.000000 -0.1138478491494694 20 1.000000 0.0000000000000000 20 2.000000 0.0000000000000000 20 5.000000 0.0000000000277033 20 10.000000 0.0000115133692478 20 50.000000 -0.1167043527595797 BESSEL_JX_VALUES_TEST: BESSEL_JX_VALUES stores values of the Bessel Jn function for NONINTEGER order. N X JN(X) 0.500000 0.200000 3.5445074421140110e-01 0.500000 1.000000 6.7139670714180311e-01 0.500000 2.000000 5.1301613656182776e-01 0.500000 2.500000 3.0200490606236569e-01 0.500000 3.000000 6.5008182877375781e-02 0.500000 5.000000 -3.4216798479816180e-01 0.500000 10.000000 -1.3726373575505049e-01 0.500000 20.000000 1.6288076385502989e-01 1.500000 1.000000 2.4029783912342700e-01 1.500000 2.000000 4.9129377868716229e-01 1.500000 5.000000 -1.6965130614474080e-01 1.500000 10.000000 1.9798249275589311e-01 1.500000 50.000000 -1.0947687298831800e-01 2.500000 1.000000 4.9496810228477940e-02 2.500000 2.000000 2.2392453146891581e-01 2.500000 5.000000 2.4037720111131741e-01 2.500000 10.000000 1.9665848358181839e-01 2.500000 50.000000 2.3037219509625530e-02 1.250000 1.000000 3.3141455085589039e-01 1.250000 2.000000 5.4617342404028402e-01 1.250000 5.000000 -2.6165841520941241e-01 1.250000 10.000000 1.2960355137912891e-01 1.250000 50.000000 -1.1174321719335520e-01 2.750000 1.000000 3.1426235705279353e-02 2.750000 2.000000 1.7179221927465271e-01 2.750000 5.000000 3.1266340695447858e-01 2.750000 10.000000 1.3402891193043640e-01 2.750000 50.000000 6.2359671351064447e-02 BESSEL_K0_VALUES_TEST: BESSEL_K0_VALUES stores values of the Bessel K0 function. X K0(X) 0.100000 2.4270690247020168 0.200000 1.7527038555281460 0.400000 1.1145291345244339 0.600000 0.7775220919047293 0.800000 0.5653471052658957 1.000000 0.4210244382407083 1.200000 0.3185082202865936 1.400000 0.2436550611815419 1.600000 0.1879547519693323 1.800000 0.1459314004898280 2.000000 0.1138938727495334 2.500000 0.0623475532003662 3.000000 0.0347395043862792 3.500000 0.0195988971703685 4.000000 0.0111596760858530 4.500000 0.0063998572432340 5.000000 0.0036910983340426 6.000000 0.0012439943280131 8.000000 0.0001464707052228 10.000000 0.0000177800623162 BESSEL_KO_INT_VALUES_TEST: BESSEL_K0_INT_VALUES stores values of the integral of the Bessel function K0. X FX 0.000977 0.0078587929563467 0.003906 0.0260199916173306 0.062500 0.2431184223754117 0.125000 0.3999963375048051 0.500000 0.9271025209311491 1.000000 1.2425098486237782 2.000000 1.4736757343168287 4.000000 1.5606495706051742 5.000000 1.5673873907283660 6.000000 1.5696345532693743 6.500000 1.5701153443250786 8.000000 1.5706574852894437 10.000000 1.5707793116159789 12.000000 1.5707942066465768 15.000000 1.5707962315469193 20.000000 1.5707963262340150 30.000000 1.5707963267948757 50.000000 1.5707963267948966 80.000000 1.5707963267948966 100.000000 1.5707963267948966 BESSEL_K1_VALUES_TEST: BESSEL_K1_VALUES stores values of the Bessel K1 function. X K1(X) 0.100000 9.8538447808706060 0.200000 4.7759725432204716 0.400000 2.1843544247326871 0.600000 1.3028349397635020 0.800000 0.8617816344721803 1.000000 0.6019072301972346 1.200000 0.4345923910607150 1.400000 0.3208359022298758 1.600000 0.2406339113576119 1.800000 0.1826230998017470 2.000000 0.1398658818165224 2.500000 0.0738908163477471 3.000000 0.0401564311281942 3.500000 0.0222393929259238 4.000000 0.0124834988872684 4.500000 0.0070780949089681 5.000000 0.0040446134454522 6.000000 0.0013439197177355 8.000000 0.0001553692118050 10.000000 0.0000186487734538 BESSEL_KN_VALUES_TEST: BESSEL_KN_VALUES stores values of the Bessel Kn function. N X KN(X) 2 0.200000 4.9512429287732871e+01 2 1.000000 1.6248388986351769e+00 2 2.000000 2.5375975456605587e-01 2 2.500000 1.2146020627856380e-01 2 3.000000 6.1510458471742038e-02 2 5.000000 5.3089437122234599e-03 2 10.000000 2.1509817006932770e-05 2 20.000000 6.3295436122922281e-10 3 1.000000 7.1012628247379448e+00 3 2.000000 6.4738539094863423e-01 3 5.000000 8.2917684152309327e-03 3 10.000000 2.7252700256598691e-05 3 50.000000 3.7279367738262112e-23 5 1.000000 3.6096058960124071e+02 5 2.000000 9.4310491005964678e+00 5 5.000000 3.2706273712031858e-02 5 10.000000 5.7541849985312281e-05 5 50.000000 4.3671822541009859e-23 10 1.000000 1.8071328990102950e+08 10 2.000000 1.6248240397955911e+05 10 5.000000 9.7585628291778104e+00 10 10.000000 1.6142553003906700e-03 10 50.000000 9.1509882099879962e-23 20 1.000000 6.2943693604245352e+22 20 2.000000 5.7708568527002408e+16 20 5.000000 4.8270005206214851e+08 20 10.000000 1.7874427820770549e+02 20 50.000000 1.7061483797220349e-21 BESSEL_KX_VALUES_TEST: BESSEL_KX_VALUES stores values of the Bessel In function for NONINTEGER order. N X KN(X) 0.500000 0.200000 2.2944893397984751e+00 0.500000 1.000000 4.6106850444789460e-01 0.500000 2.000000 1.1993777196806139e-01 0.500000 2.500000 6.5065943154009986e-02 0.500000 3.000000 3.6025985131764589e-02 0.500000 5.000000 3.7766133746428830e-03 0.500000 10.000000 1.7993478093705181e-05 0.500000 20.000000 5.7763739747074450e-10 1.500000 1.000000 9.2213700889578909e-01 1.500000 2.000000 1.7990665795209221e-01 1.500000 5.000000 4.5319360495714592e-03 1.500000 10.000000 1.9792825903075699e-05 1.500000 50.000000 3.4869924973662158e-23 2.500000 1.000000 3.2274795311352622e+00 2.500000 2.000000 3.8979775889619972e-01 2.500000 5.000000 6.4957750043857579e-03 2.500000 10.000000 2.3931325864627889e-05 2.500000 50.000000 3.6278396452990477e-23 1.250000 1.000000 7.3114518792021144e-01 1.250000 2.000000 1.5674754783939321e-01 1.250000 5.000000 4.2573895281774613e-03 1.250000 10.000000 1.9155410658695629e-05 1.250000 50.000000 3.4633375935693059e-23 2.750000 1.000000 4.7311848399195409e+00 2.750000 2.000000 4.9768762255147581e-01 2.750000 5.000000 7.3008646109411629e-03 2.750000 10.000000 2.5464212941064581e-05 2.750000 50.000000 3.6752756779136562e-23 BESSEL_Y0_VALUES_TEST: BESSEL_Y0_VALUES stores values of the Bessel Y0 function. X Y0(X) 0.100000 -1.5342386513503670 1.000000 0.0882569642156770 2.000000 0.5103756726497451 3.000000 0.3768500100127904 4.000000 -0.0169407393250650 5.000000 -0.3085176252490338 6.000000 -0.2881946839815792 7.000000 -0.0259497439672093 8.000000 0.2235214893875662 9.000000 0.2499366982850247 10.000000 0.0556711672835994 11.000000 -0.1688473238920795 12.000000 -0.2252373126343614 13.000000 -0.0782078645278759 14.000000 0.1271925685821837 15.000000 0.2054642960389183 BESSEL_YO_INT_VALUES_TEST: BESSEL_Y0_INT_VALUES stores values of the integral of the Bessel function Y0. X FX 0.001953 -0.0091442642860172 0.007812 -0.0296820473903976 0.125000 -0.2539143127658539 0.500000 -0.5617954559146403 1.000000 -0.6370693766074231 2.000000 -0.2821928500851009 4.000000 0.3836696478531256 6.000000 -0.1259506128579893 10.000000 0.2412903183226668 16.000000 0.1713806975762704 16.250000 0.1895814262713408 17.000000 0.1720384613644971 20.000000 -0.1682159767721503 25.000000 -0.0936079273514290 30.000000 0.0882297119480367 40.000000 -0.0089324662736274 50.000000 -0.0548140710000635 70.000000 -0.0949582460034664 100.000000 -0.0195980648534050 125.000000 -0.0083084772357155 BESSEL_Y0_SPHERICAL_VALUES_TEST: BESSEL_Y0_SPHERICAL_VALUES stores values of the y0 spherical Bessel function. X FX 0.100000 -9.9500416527802589 0.200000 -4.9003328892062079 0.400000 -2.3026524850072132 0.600000 -1.3755593581827970 0.800000 -0.8708833866839568 1.000000 -0.5403023058681397 1.200000 -0.3019647953972280 1.400000 -0.1214051020716007 1.600000 0.0182497014383055 1.800000 0.1262233859406039 2.000000 0.2080734182735712 2.200000 0.2675005078433390 2.400000 0.3072473814755190 2.600000 0.3295725974495951 2.800000 0.3365079788102351 3.000000 0.3299974988668152 3.200000 0.3119671174358603 3.400000 0.2843524095821944 3.600000 0.2490995600928186 3.800000 0.2081493978722149 4.000000 0.1634109052159030 BESSEL_Y1_VALUES_TEST: BESSEL_Y1_VALUES stores values of the Bessel Y1 function. X Y1(X) 0.100000 -6.4589510947020274 1.000000 -0.7812128213002887 2.000000 -0.1070324315409375 3.000000 0.3246744247918000 4.000000 0.3979257105571000 5.000000 0.1478631433912268 6.000000 -0.1750103443003983 7.000000 -0.3026672370241849 8.000000 -0.1580604617312475 9.000000 0.1043145751967159 10.000000 0.2490154242069539 11.000000 0.1637055374149429 12.000000 -0.0570992182608965 13.000000 -0.2100814084206935 14.000000 -0.1666448418561723 15.000000 0.0210736280368735 BESSEL_Y1_SPHERICAL_VALUES_TEST: BESSEL_Y1_SPHERICAL_VALUES stores values of the y1 spherical Bessel function. X FX 0.100000 -100.4987506942708961 0.200000 -25.4950111000063515 0.400000 -6.7301770682896578 0.600000 -3.2336697192963881 0.800000 -1.9852993469793490 1.000000 -1.3817732906760360 1.200000 -1.0283365678037120 1.400000 -0.7906105943286149 1.600000 -0.6133274385019998 1.800000 -0.4709023582986618 2.000000 -0.3506120042760553 2.200000 -0.2459072254437506 2.400000 -0.1534232496148467 2.600000 -0.0715110670661035 2.800000 0.0005427959479750 3.000000 0.0629591636023160 3.200000 0.1157316440198251 3.400000 0.1587922092967723 3.600000 0.1921166676076864 3.800000 0.2157913917934037 4.000000 0.2300533501309578 BESSEL_YN_VALUES_TEST: BESSEL_YN_VALUES stores values of the Bessel Yn function. N X YN(X) 2 1.000000 -1.6506826068162539e+00 2 2.000000 -6.1740810419068270e-01 2 5.000000 3.6766288260552449e-01 2 10.000000 -5.8680824422086154e-03 2 50.000000 9.5793168727596495e-02 5 1.000000 -2.6040586662581222e+02 5 2.000000 -9.9359891284819746e+00 5 5.000000 -4.5369482249110188e-01 5 10.000000 1.3540304768936229e-01 5 50.000000 -7.8548413913081649e-02 10 1.000000 -1.2161801427868921e+08 10 2.000000 -1.2918454220803930e+05 10 5.000000 -2.5129110095610098e+01 10 10.000000 -3.5981415218340268e-01 10 50.000000 5.7238971820535141e-03 20 1.000000 -4.1139703148355049e+22 20 2.000000 -4.0816513889983672e+16 20 5.000000 -5.9339652969143212e+08 20 10.000000 -1.5974838482696259e+03 20 50.000000 1.6442633948115778e-02 BESSEL_YX_VALUES_TEST: BESSEL_YX_VALUES stores values of the Bessel Yn function for NONINTEGER order. N X YN(X) 0.500000 0.200000 -1.7485604169618760e+00 0.500000 1.000000 -4.3109886801837610e-01 0.500000 2.000000 2.3478571040624849e-01 0.500000 2.500000 4.0427830223905692e-01 0.500000 3.000000 4.5604882079463321e-01 0.500000 5.000000 -1.0121770918510840e-01 0.500000 10.000000 2.1170886633139821e-01 0.500000 20.000000 -7.2806904785061854e-02 1.500000 1.000000 -1.1024955751601790e+00 1.500000 2.000000 -3.9562328135870350e-01 1.500000 5.000000 3.2192444296114009e-01 1.500000 10.000000 1.5843462238819031e-01 1.500000 50.000000 2.7428136761913819e-02 2.500000 1.000000 -2.8763878574621611e+00 2.500000 2.000000 -8.2822063244430366e-01 2.500000 5.000000 2.9437237496179253e-01 2.500000 10.000000 -1.6417847961494109e-01 2.500000 50.000000 1.1053044455625440e-01 1.250000 1.000000 -9.3196592519698807e-01 1.250000 2.000000 -2.6094450109489331e-01 1.250000 5.000000 2.4927963621858809e-01 1.250000 10.000000 2.1744103014167329e-01 1.250000 50.000000 -1.5785766505572289e-02 2.750000 1.000000 -4.0234533015010276e+00 2.750000 2.000000 -9.5889986947523886e-01 2.750000 5.000000 2.2642603610473669e-01 2.750000 10.000000 -2.1936177365667600e-01 2.750000 50.000000 9.4139883445150771e-02 BETA_VALUES_TEST: BETA_VALUES stores values of the Beta function. X Y BETA(X,Y) 0.200000 1.000000 5.0000000000000000 0.400000 1.000000 2.5000000000000000 0.600000 1.000000 1.6666666666666670 0.800000 1.000000 1.2500000000000000 1.000000 0.200000 5.0000000000000000 1.000000 0.400000 2.5000000000000000 1.000000 1.000000 1.0000000000000000 2.000000 2.000000 0.1666666666666667 3.000000 3.000000 0.0333333333333333 4.000000 4.000000 0.0071428571428571 5.000000 5.000000 0.0015873015873016 6.000000 2.000000 0.0238095238095238 6.000000 3.000000 0.0059523809523810 6.000000 4.000000 0.0019841269841270 6.000000 5.000000 0.0007936507936508 6.000000 6.000000 0.0003607503607504 7.000000 7.000000 0.0000832500832501 BETA_CDF_VALUES_TEST: BETA_CDF_VALUES stores values of the BETA CDF. A B X FX 0.500000 0.500000 0.010000 0.0637685608585199 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1.0000000000000000 1.000000 0.500000 0.000000 0.0000000000000000 1.000000 0.500000 0.010000 0.0050125628933800 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5000000000000000 2.000000 2.000000 0.100000 0.0280000000000000 2.000000 2.000000 0.200000 0.1040000000000000 2.000000 2.000000 0.300000 0.2160000000000000 2.000000 2.000000 0.400000 0.3520000000000000 2.000000 2.000000 0.500000 0.5000000000000000 2.000000 2.000000 0.600000 0.6480000000000000 2.000000 2.000000 0.700000 0.7840000000000000 2.000000 2.000000 0.800000 0.8960000000000000 2.000000 2.000000 0.900000 0.9720000000000000 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.0897827148437500 10.000000 5.000000 1.000000 1.0000000000000000 10.000000 10.000000 0.500000 0.5000000000000000 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5000000000000000 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.3600000000000000 1.000000 3.000000 0.200000 0.4880000000000000 1.000000 4.000000 0.200000 0.5904000000000000 1.000000 5.000000 0.200000 0.6723200000000000 2.000000 2.000000 0.300000 0.2160000000000000 3.000000 2.000000 0.300000 0.0837000000000000 4.000000 2.000000 0.300000 0.0307800000000000 5.000000 2.000000 0.300000 0.0109350000000000 1.306250 11.756200 0.225609 0.9188846846205180 1.306250 11.756200 0.033557 0.2105297748941900 1.306250 11.756200 0.029522 0.1824130512500673 BETA_INC_VALUES_TEST: BETA_INC_VALUES stores values of the incomplete Beta function. A B X BETA_INC(A,B)(X) 0.500000 0.500000 0.010000 0.0637685608585199 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1.0000000000000000 1.000000 0.500000 0.000000 0.0000000000000000 1.000000 0.500000 0.010000 0.0050125628933800 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5000000000000000 2.000000 2.000000 0.100000 0.0280000000000000 2.000000 2.000000 0.200000 0.1040000000000000 2.000000 2.000000 0.300000 0.2160000000000000 2.000000 2.000000 0.400000 0.3520000000000000 2.000000 2.000000 0.500000 0.5000000000000000 2.000000 2.000000 0.600000 0.6480000000000000 2.000000 2.000000 0.700000 0.7840000000000000 2.000000 2.000000 0.800000 0.8960000000000000 2.000000 2.000000 0.900000 0.9720000000000000 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.0897827148437500 10.000000 5.000000 1.000000 1.0000000000000000 10.000000 10.000000 0.500000 0.5000000000000000 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5000000000000000 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.3600000000000000 1.000000 3.000000 0.200000 0.4880000000000000 1.000000 4.000000 0.200000 0.5904000000000000 1.000000 5.000000 0.200000 0.6723200000000000 2.000000 2.000000 0.300000 0.2160000000000000 3.000000 2.000000 0.300000 0.0837000000000000 4.000000 2.000000 0.300000 0.0307800000000000 5.000000 2.000000 0.300000 0.0109350000000000 1.306250 11.756200 0.225609 0.9188846846205180 1.306250 11.756200 0.033557 0.2105297748941900 1.306250 11.756200 0.029522 0.1824130512500673 BETA_LOG_VALUES_TEST: BETA_LOG_VALUES stores values of the logarithm of the Beta function. X Y BETA_LOG(X,Y) 0.200000 1.000000 1.6094379124341001 0.400000 1.000000 0.9162907318741551 0.600000 1.000000 0.5108256237659907 0.800000 1.000000 0.2231435513142098 1.000000 0.200000 1.6094379124341001 1.000000 0.400000 0.9162907318741551 1.000000 1.000000 0.0000000000000000 2.000000 2.000000 -1.7917594692280550 3.000000 3.000000 -3.4011973816621550 4.000000 4.000000 -4.9416424226093039 5.000000 5.000000 -6.4457198193855776 6.000000 2.000000 -3.7376696182833680 6.000000 3.000000 -5.1239639794032588 6.000000 4.000000 -6.2225762680713688 6.000000 5.000000 -7.1388669999455239 6.000000 6.000000 -7.9273243603097940 7.000000 7.000000 -9.3936614291032203 BETA_NONCENTRAL_CDF_VALUES_TEST: BETA_NONCENTRAL_CDF_VALUES stores values of the noncentral BETA CDF. A B LAMBDA X FX 5.000000 5.000000 54.000000 0.864000 0.4563021000000000 5.000000 5.000000 140.000000 0.900000 0.1041337000000000 5.000000 5.000000 170.000000 0.956000 0.6022353000000000 10.000000 10.000000 54.000000 0.868600 0.9187770000000000 10.000000 10.000000 140.000000 0.900000 0.6008106000000000 10.000000 10.000000 250.000000 0.900000 0.0902850000000000 20.000000 20.000000 54.000000 0.878700 0.9998655000000000 20.000000 20.000000 140.000000 0.900000 0.9925997000000000 20.000000 20.000000 250.000000 0.922000 0.9641111999999999 10.000000 20.000000 150.000000 0.868000 0.9376626573000000 10.000000 10.000000 120.000000 0.900000 0.7306817858000000 15.000000 5.000000 80.000000 0.880000 0.1604256918000000 20.000000 10.000000 110.000000 0.850000 0.1867485313000000 20.000000 30.000000 65.000000 0.660000 0.6559386874000001 20.000000 50.000000 130.000000 0.720000 0.9796881486000000 30.000000 20.000000 80.000000 0.720000 0.1162386423000000 30.000000 40.000000 130.000000 0.800000 0.9930430054000000 10.000000 5.000000 20.000000 0.644000 0.0506899273000000 10.000000 10.000000 54.000000 0.700000 0.1030959706000000 10.000000 30.000000 80.000000 0.780000 0.9978417832000001 15.000000 20.000000 120.000000 0.760000 0.2555552369000000 10.000000 5.000000 55.000000 0.795000 0.0668307064000000 12.000000 17.000000 64.000000 0.560000 0.0113601067000000 30.000000 30.000000 140.000000 0.800000 0.7813366615000000 35.000000 30.000000 20.000000 0.670000 0.8867126477000000 BETA_PDF_VALUES_TEST: BETA_PDF_VALUES stores values of the BETA PDF. ALPHA BETA X FX 1.09209 4.78159 0.866722 0.002826137156803199 2.80848 2.07654 0.0460776 0.04208950342768649 1.28789 0.549784 0.0221162 0.2184064957817208 3.16983 0.308636 0.458254 0.1335142301445414 2.00653 3.77337 0.832083 0.1070571849830009 0.00919186 4.48752 0.352059 0.005796394377470491 0.472724 0.0680845 0.898529 0.5518796772414584 4.20424 0.61552 -0.0169242 0 1.30151 4.56242 0.0971888 2.87907465409348 1.75814 4.11444 0.262167 2.126992854611924 BINOMIAL_VALUES_TEST: BINOMIAL_VALUES returns values of the binomial numbers. A B C(A,B) 1 0 1 6 1 6 6 3 20 6 5 6 15 1 15 15 3 455 15 5 3003 15 7 6435 15 9 5005 15 11 1365 15 13 105 25 1 25 25 3 2300 25 5 53130 25 7 480700 25 9 2042975 25 11 4457400 25 13 5200300 25 15 3268760 25 17 1081575 BINOMIAL_CDF_VALUES_TEST: BINOMIAL_CDF_VALUES returns values of the Binomial Cumulative Density Function. A B X CDF(A,B)(X) 2 0.050000 0 0.9025000000000000 2 0.050000 1 0.9975000000000001 2 0.050000 2 1.0000000000000000 2 0.500000 0 0.2500000000000000 2 0.500000 1 0.7500000000000000 4 0.250000 0 0.3164062500000000 4 0.250000 1 0.7382812500000000 4 0.250000 2 0.9492187500000000 4 0.250000 3 0.9960937500000000 10 0.050000 4 0.9999363101685547 10 0.100000 4 0.9983650626000000 10 0.150000 4 0.9901259090013672 10 0.200000 4 0.9672065023999999 10 0.250000 4 0.9218730926513672 10 0.300000 4 0.8497316673999999 10 0.400000 4 0.6331032576000000 10 0.500000 4 0.3769531250000000 BINOMIAL_PDF_VALUES_TEST: BINOMIAL_PDF_VALUES returns values of the Binomial Probability Density Function. A B X PDF(A,B)(X) 5 0.829509 5 0.3927408939646697 12 0.066119 5 0.0006199968732461 6 0.043829 0 0.7642112247331240 13 0.449539 0 0.0004260353334365 9 0.797287 7 0.3029482891457940 1 0.350752 1 0.3507523379805466 2 0.859097 0 0.0198536961920256 17 0.007512 2 0.0068543888796466 6 0.113664 6 0.0000021564464464 8 0.267132 7 0.0005691150511772 BIVARIATE_NORMAL_CDF_VALUES_TEST: BIVARIATE_NORMAL_CDF_VALUES stores values of the bivariate normal CDF. X Y R F(R)(X,Y) -2.000000 1.000000 0.500000 0.0226032721856987 -1.000000 1.000000 0.500000 0.1548729518584100 0.000000 1.000000 0.500000 0.4687428083352184 1.000000 1.000000 0.500000 0.7452035868929476 2.000000 1.000000 0.500000 0.8318608306874188 3.000000 1.000000 0.500000 0.8410314261134202 -0.200000 0.500000 -0.900000 0.1377019384919464 -0.200000 0.500000 -0.800000 0.1621749501739030 -0.200000 0.500000 -0.700000 0.1827411243233119 -0.200000 0.500000 -0.600000 0.2010067421506235 -0.200000 0.500000 -0.500000 0.2177751155265290 -0.200000 0.500000 -0.400000 0.2335088436446962 -0.200000 0.500000 -0.300000 0.2485057781834286 -0.200000 0.500000 -0.200000 0.2629747825154868 -0.200000 0.500000 -0.100000 0.2770729823404738 -0.200000 0.500000 0.000000 0.2909261168683812 -0.200000 0.500000 0.100000 0.3046406378726738 -0.200000 0.500000 0.200000 0.3183113449213638 -0.200000 0.500000 0.300000 0.3320262544108028 -0.200000 0.500000 0.400000 0.3458686754647614 -0.200000 0.500000 0.500000 0.3599150462310668 -0.200000 0.500000 0.600000 0.3742210899871168 -0.200000 0.500000 0.700000 0.3887706405282320 -0.200000 0.500000 0.800000 0.4032765198361344 -0.200000 0.500000 0.900000 0.4162100291953678 1.000000 0.500000 0.673000 0.6508271498838664 2.000000 1.000000 0.500000 0.8318608306874188 0.000000 0.000000 -1.000000 0.0000000000000000 0.000000 0.000000 -0.500000 0.1666666666539970 0.000000 0.000000 0.000000 0.2500000000000000 0.000000 0.000000 0.500000 0.3333333333328906 0.000000 0.000000 1.000000 0.5000000000000000 1.000000 1.000000 0.500000 0.7452035868929476 1.000000 -1.000000 0.500000 0.1548729518584100 -1.000000 1.000000 0.500000 0.1548729518584100 -1.000000 -1.000000 0.500000 0.0625140947043165 1.000000 1.000000 0.500000 0.7452035868929476 1.000000 -1.000000 0.500000 0.1548729518584100 -1.000000 1.000000 0.500000 0.1548729518584100 -1.000000 -1.000000 0.500000 0.0625140947043165 0.707107 0.707107 0.500000 0.6337020457912916 CATALAN_VALUES_TEST: CATALAN_VALUES returns values of the Catalan numbers. N C(N) 0 1 1 1 2 2 3 5 4 14 5 42 6 132 7 429 8 1430 9 4862 10 16796 CAUCHY_CDF_VALUES_TEST: CAUCHY_CDF_VALUES stores values of the Cauchy CDF. MU SIGMA X FX 1.000000 0.500000 1.000000 0.5000000000000000 1.000000 0.500000 2.000000 0.8524163823495667 1.000000 0.500000 3.000000 0.9220208696226307 1.000000 0.500000 4.000000 0.9474315432887466 1.000000 2.000000 2.000000 0.6475836176504333 1.000000 3.000000 2.000000 0.6024163823495667 1.000000 4.000000 2.000000 0.5779791303773693 1.000000 5.000000 2.000000 0.5628329581890013 2.000000 2.000000 3.000000 0.6475836176504333 3.000000 2.000000 3.000000 0.5000000000000000 4.000000 2.000000 3.000000 0.3524163823495667 5.000000 2.000000 3.000000 0.2500000000000000 CBRT_VALUES_TEST: CBRT_VALUES stores values of the cube root. X CBRT(X) 0.000000 0.0000000000000000 -0.000000 -0.0020082988563383 0.090000 0.4481404746557165 -0.100000 -0.4641588833612779 0.400000 0.7368062997280773 -1.000000 -1.0000000000000000 2.000000 1.2599210498948732 -3.000000 -1.4422495703074083 3.141593 1.4645918875615234 -19.000000 -2.6684016487219449 29.000000 3.0723168256858471 -71.000000 -4.1408177494228529 97.000000 4.5947008922070394 -123456789.000000 -497.9338592181744616 CHEBY_T_POLY_VALUES_TEST: CHEBY_T_POLY_VALUES returns values of the Chebyshev T polynomials. N X T(N)(X) -1 0.800000 0.0000000000000000 0 0.800000 1.0000000000000000 1 0.800000 0.8000000000000000 2 0.800000 0.2800000000000000 3 0.800000 -0.3520000000000000 4 0.800000 -0.8431999999999999 5 0.800000 -0.9971200000000000 6 0.800000 -0.7521920000000000 7 0.800000 -0.2063872000000000 8 0.800000 0.4219724800000000 9 0.800000 0.8815431680000000 10 0.800000 0.9884965888000000 11 0.800000 0.7000513740800000 12 0.800000 0.1315856097280000 CHEBY_T01_POLY_VALUES_TEST: CHEBY_T01_POLY_VALUES returns values of the shifted Chebyshev T polynomials. N X T01(N)(X) -1 0.850000 0.0000000000000000 0 0.850000 1.0000000000000000 1 0.850000 0.7000000000000000 2 0.850000 -0.0200000000000000 3 0.850000 -0.7280000000000000 4 0.850000 -0.9992000000000000 5 0.850000 -0.6708800000000000 6 0.850000 0.0599680000000000 7 0.850000 0.7548352000000000 8 0.850000 0.9968012800000000 9 0.850000 0.6406865920000000 10 0.850000 -0.0998400512000000 11 0.850000 -0.7804626636799999 12 0.850000 -0.9928076779520000 7 0.000000 -1.0000000000000000 7 0.100000 0.2063872000000000 7 0.200000 -0.9784704000000000 7 0.300000 0.2580224000000000 7 0.400000 0.9870208000000000 7 0.500000 0.0000000000000000 7 0.600000 -0.9870208000000000 7 0.700000 -0.2580224000000000 7 0.800000 0.9784704000000000 7 0.900000 -0.2063872000000000 7 1.000000 1.0000000000000000 CHEBY_U_POLY_VALUES_TEST: CHEBY_U_POLY_VALUES returns values of the Chebyshev U polynomials. N X U(N)(X) -1 0.800000 0.0000000000000000 0 0.800000 1.0000000000000000 1 0.800000 1.6000000000000001 2 0.800000 1.5600000000000001 3 0.800000 0.8960000000000000 4 0.800000 -0.1264000000000000 5 0.800000 -1.0982400000000001 6 0.800000 -1.6307840000000000 7 0.800000 -1.5110144000000001 8 0.800000 -0.7868390400000000 9 0.800000 0.2520719360000000 10 0.800000 1.1901541376000000 11 0.800000 1.6521746841600000 12 0.800000 1.4533253570560001 CHEBY_U01_POLY_VALUES_TEST: CHEBY_U01_POLY_VALUES returns values of the shifted Chebyshev U polynomials. N X U01(N)(X) -1 0.850000 0.0000000000000000 0 0.850000 1.0000000000000000 1 0.850000 1.3999999999999999 2 0.850000 0.9600000000000000 3 0.850000 -0.0560000000000000 4 0.850000 -1.0384000000000000 5 0.850000 -1.3977599999999999 6 0.850000 -0.9184639999999999 7 0.850000 0.1119104000000000 8 0.850000 1.0751385600000001 9 0.850000 1.3932835840000000 10 0.850000 0.8754584576000000 11 0.850000 -0.1676417433600000 12 0.850000 -1.1101568983040000 7 0.000000 -8.0000000000000000 7 0.100000 1.5110144000000001 7 0.200000 -1.1332608000000000 7 0.300000 -0.1636352000000000 7 0.400000 1.0198016000000001 7 0.500000 0.0000000000000000 7 0.600000 -1.0198016000000001 7 0.700000 0.1636352000000000 7 0.800000 1.1332608000000000 7 0.900000 -1.5110144000000001 7 1.000000 8.0000000000000000 CHEBY_V_POLY_VALUES_TEST: CHEBY_V_POLY_VALUES returns values of the Chebyshev V polynomials. N X V(N)(X) -1 0.800000 0.0000000000000000 0 0.800000 1.0000000000000000 1 0.800000 0.6000000000000000 2 0.800000 -0.0400000000000000 3 0.800000 -0.6640000000000000 4 0.800000 -1.0224000000000000 5 0.800000 -0.9718400000000000 6 0.800000 -0.5325440000000000 7 0.800000 0.1197696000000000 8 0.800000 0.7241753600000000 9 0.800000 1.0389109759999999 10 0.800000 0.9380822016000000 11 0.800000 0.4620205465600000 12 0.800000 -0.1988493271040000 CHEBY_V01_POLY_VALUES_TEST: CHEBY_V01_POLY_VALUES returns values of the shifted Chebyshev V polynomials. N X V01(N)(X) -1 0.850000 0.0000000000000000 0 0.850000 1.0000000000000000 1 0.850000 0.4000000000000000 2 0.850000 -0.4400000000000000 3 0.850000 -1.0160000000000000 4 0.850000 -0.9824000000000001 5 0.850000 -0.3593600000000000 6 0.850000 0.4792960000000000 7 0.850000 1.0303743999999999 8 0.850000 0.9632281600000000 9 0.850000 0.3181450240000000 10 0.850000 -0.5178251264000000 11 0.850000 -1.0431002009599999 12 0.850000 -0.9425151549440000 7 0.000000 -15.0000000000000000 7 0.100000 3.1417983999999999 7 0.200000 -1.3912447999999999 7 0.300000 -1.2177792000000001 7 0.400000 1.1837055999999999 7 0.500000 1.0000000000000000 7 0.600000 -0.8558976000000000 7 0.700000 -0.8905088000000000 7 0.800000 0.8752768000000000 7 0.900000 0.1197696000000000 7 1.000000 1.0000000000000000 CHEBY_W_POLY_VALUES_TEST: CHEBY_W_POLY_VALUES returns values of the Chebyshev W polynomials. N X W(N)(X) -1 0.800000 0.0000000000000000 0 0.800000 1.0000000000000000 1 0.800000 2.6000000000000001 2 0.800000 3.1600000000000001 3 0.800000 2.4560000000000000 4 0.800000 0.7696000000000000 5 0.800000 -1.2246400000000000 6 0.800000 -2.7290239999999999 7 0.800000 -3.1417983999999999 8 0.800000 -2.2978534399999999 9 0.800000 -0.5347671040000000 10 0.800000 1.4422260736000001 11 0.800000 2.8423288217599998 12 0.800000 3.1055000412160001 CHEBY_W01_POLY_VALUES_TEST: CHEBY_W01_POLY_VALUES returns values of the shifted Chebyshev W polynomials. N X W01(N)(X) -1 0.850000 0.0000000000000000 0 0.850000 1.0000000000000000 1 0.850000 2.3999999999999999 2 0.850000 2.3599999999999999 3 0.850000 0.9040000000000000 4 0.850000 -1.0944000000000000 5 0.850000 -2.4361600000000001 6 0.850000 -2.3162240000000001 7 0.850000 -0.8065536000000000 8 0.850000 1.1870489600000000 9 0.850000 2.4684221439999998 10 0.850000 2.2687420415999999 11 0.850000 0.7078167142400000 12 0.850000 -1.2777986416639999 7 0.000000 -1.0000000000000000 7 0.100000 -0.1197696000000000 7 0.200000 -0.8752768000000000 7 0.300000 0.8905088000000000 7 0.400000 0.8558976000000000 7 0.500000 -1.0000000000000000 7 0.600000 -1.1837055999999999 7 0.700000 1.2177792000000001 7 0.800000 1.3912447999999999 7 0.900000 -3.1417983999999999 7 1.000000 15.0000000000000000 CHI_VALUES_TEST: CHI_VALUES stores values of the hyperbolic Cosine Integral function CHI(X). X CHI(X) 0.500000 -0.0527768449564936 0.600000 0.1577508933739787 0.700000 0.3455691756953907 0.800000 0.5183999848333914 0.900000 0.6813138871854340 1.000000 0.8378669409802082 1.200000 1.1418419241705950 1.400000 1.4454940757896440 1.600000 1.7595058076609651 1.800000 2.0925772140620320 2.000000 2.4526669226469151 2.500000 3.5244254883541650 3.000000 4.9603920947656102 3.500000 6.9591919276473932 4.000000 9.8135475588231866 4.500000 13.9658116485924300 CHI_SQUARE_CDF_VALUES_TEST: CHI_SQUARE_CDF_VALUES returns values of the Chi-Squared Cumulative Density Function. N X CHI_CDF(X) 1 0.010000 0.0796556745540580 2 0.010000 0.0049875208073177 1 0.020000 0.1124629160182849 2 0.020000 0.0099501662508319 1 0.400000 0.4729107431344619 2 0.400000 0.1812692469220181 3 0.400000 0.0597575051606393 4 0.400000 0.0175230963064218 1 1.000000 0.6826894921370859 2 1.000000 0.3934693402873666 3 1.000000 0.1987480430987992 4 1.000000 0.0902040104310499 5 1.000000 0.0374342267527036 3 2.000000 0.4275932955291202 3 3.000000 0.6083748237289111 3 4.000000 0.7385358700508894 3 5.000000 0.8282028557032669 3 6.000000 0.8883897749052874 10 1.000000 0.0001721156299558 10 2.000000 0.0036598468273437 10 3.000000 0.0185759362221407 CHI_SQUARE_PDF_VALUES_TEST: CHI_SQUARE_PDF_VALUES returns values of the Chi-Squared Probability Density Function. DF X CHI_PDF(X) 1 0.01 3.969525474770117 2 0.01 0.4975062395963412 1 0.02 2.792879016972342 2 0.02 0.4950249168745841 1 0.4 0.5164415474672784 2 0.4 0.4093653765389909 3 0.4 0.2065766189869113 4 0.4 0.08187307530779819 1 1 0.2419707245191434 2 1 0.3032653298563167 3 1 0.2419707245191434 4 1 0.1516326649281584 5 1 0.08065690817304777 3 2 0.2075537487102974 3 3 0.1541803298037693 3 4 0.1079819330263761 3 5 0.07322491280963248 3 6 0.04865217332964145 10 1 0.0007897534631674914 10 2 0.00766415502440505 10 3 0.02353325907815472 CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST: CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral Chi-Squared Cumulative Density Function. X LAMBDA DF CDF 1.000000 0.500000 3 8.3994442693982607e-01 2.000000 0.500000 3 6.9590603004351392e-01 3.000000 0.500000 3 5.3508796970788475e-01 1.000000 1.000000 3 7.6478414963103125e-01 2.000000 1.000000 3 6.2064365321954362e-01 3.000000 1.000000 3 4.6916673753731802e-01 1.000000 5.000000 3 3.0708843459375690e-01 2.000000 5.000000 3 2.2038180929909029e-01 3.000000 5.000000 3 1.5002518955815189e-01 1.000000 20.000000 3 3.0711631943357910e-03 2.000000 20.000000 3 1.7639826701318941e-03 3.000000 20.000000 3 9.8167925946250211e-04 60.000000 30.000000 60 1.6517531408662078e-02 80.000000 30.000000 60 2.0234195739504511e-04 100.000000 30.000000 60 4.9844763528540740e-07 1.000000 5.000000 5.000000e-02 1.5132524006548270e-02 2.000000 5.000000 5.000000e-02 2.0904149106143670e-03 3.000000 5.000000 5.000000e-02 2.4650212060484518e-04 10.000000 2.000000 4 2.6368350503429391e-02 10.000000 3.000000 4 1.8579832200792151e-02 10.000000 4.000000 4 1.3057365954866401e-02 10.000000 2.000000 5 5.8380395348193510e-02 10.000000 3.000000 5 4.2497844024637119e-02 10.000000 4.000000 5 3.0821377160215959e-02 10.000000 2.000000 6 1.0578782234008489e-01 10.000000 3.000000 6 7.9408429845985090e-02 10.000000 4.000000 6 5.9320108955996390e-02 8.000000 0.500000 5 2.1103956569186841e-01 CI_VALUES_TEST: CI_VALUES stores values of the Cosine Integral function CI(X). X CI(X) 0.500000 -0.1777840788066129 0.600000 -0.0222707069592798 0.700000 0.1005147070088978 0.800000 0.1982786159524672 0.900000 0.2760678304677729 1.000000 0.3374039229009681 1.200000 0.4204591828942405 1.400000 0.4620065850946773 1.600000 0.4717325169318778 1.800000 0.4568111294183369 2.000000 0.4229808287748650 2.500000 0.2858711963653835 3.000000 0.1196297860080003 3.500000 -0.0321285485124811 4.000000 -0.1409816978869304 4.500000 -0.1934911221017388 CIN_VALUES_TEST: CIN_VALUES stores values of the Cosine Integral function CIN(X). X CIN(X) 0.500000 0.0618525631482005 0.600000 0.0886607480948219 0.700000 0.1200260139539026 0.800000 0.1557934976348559 0.900000 0.1957873187759337 1.000000 0.2398117420005647 1.200000 0.3390780388012470 1.400000 0.4516813164280685 1.600000 0.5754867772153907 1.800000 0.7081912003853150 2.000000 0.8473820166866132 2.500000 1.2076352004103039 3.000000 1.5561981675616421 3.500000 1.8621071819093820 4.000000 2.1044917239083540 4.500000 2.2747841837795462 CINH_VALUES_TEST: CINH_VALUES stores values of the Hyperbolic Cosine Integral function CINH(X). X CINH(X) 0.000000 0.0000000000000000 0.500000 0.0631546707019188 0.600000 0.0913608522384365 0.700000 0.1250284547325902 0.800000 0.1643278712460683 0.900000 0.2094587379417273 1.000000 0.2606512760786754 1.200000 0.3823047024751071 1.400000 0.5318061742668980 1.600000 0.7122865135136963 1.800000 0.9275748842583805 2.000000 1.1823040771854361 2.500000 2.0309190915784781 3.000000 3.2845641411959670 3.500000 5.1292132942504933 4.000000 7.8500375328017622 4.500000 11.8845185869146306 CLAUSEN_VALUES_TEST: CLAUSEN_VALUES stores values of the Clausen function. X FX 0.001953 0.0141373528867606 0.031250 0.1395546708198128 -0.125000 -0.3849573215657424 0.500000 0.8483118777036792 1.000000 1.0139591323607684 -1.500000 -0.9392185927540921 2.000000 0.7271460508632792 2.500000 0.4335982032355328 -3.000000 -0.0980262093913014 4.000000 -0.5681439444298698 4.250000 -0.7096970178444892 -5.000000 0.9928201325469567 5.500000 -0.9812774747744737 6.000000 -0.6407826657017233 8.000000 0.8602796373323119 -10.000000 0.3907164760868021 15.000000 0.4757479392653919 20.000000 1.0105014481412877 -30.000000 0.9633208904436308 50.000000 -0.6178269948192932 CLEBSCH_GORDAN_VALUES_TEST: CLEBSCH_GORDAN_VALUES returns values of the Clebsch-Gordan coefficient. J1 J2 J3 M1 M2 M3 CG 0.50 0.50 1.00 0.50 -0.50 0.00 0.7071067811865475 0.50 0.50 1.00 0.50 0.50 1.00 1.0000000000000000 0.50 1.00 1.50 -0.50 1.00 0.50 0.5773502691896258 1.00 1.50 1.50 0.00 0.50 0.50 -0.2581988897471611 1.00 1.50 1.50 -1.00 1.50 0.50 -0.6324555320336759 1.00 1.50 1.50 0.00 1.50 1.50 -0.7745966692414834 1.00 1.00 2.00 1.00 -1.00 0.00 0.4082482904638630 1.00 1.00 2.00 0.00 0.00 0.00 0.8164965809277260 2.00 2.00 2.00 2.00 -2.00 0.00 0.5345224838248488 2.00 2.00 2.00 1.00 -1.00 0.00 0.2672612419124244 1.50 2.00 2.50 0.50 1.00 1.50 0.8944271909999159 1.50 2.00 3.50 1.50 -1.00 0.50 0.3380617018914066 COLLATZ_COUNT_VALUES_TEST: COLLATZ_COUNT_VALUES returns values of the length of the Collatz sequence that starts at N. N COLLATZ_COUNT(N) 1 1 2 2 3 8 4 3 5 6 6 9 7 17 8 4 9 20 10 7 27 112 50 25 100 26 200 27 300 17 400 28 500 111 600 18 700 83 800 29 COS_VALUES_TEST: COS_VALUES stores values of the cosine function. X FX 0.000000 1.0000000000000000 0.261799 0.9659258262890683 0.500000 0.8775825618903728 0.523599 0.8660254037844386 0.785398 0.7071067811865476 1.000000 0.5403023058681398 1.047198 0.5000000000000000 1.570796 0.0000000000000000 2.000000 -0.4161468365471424 3.000000 -0.9899924966004454 3.141593 -1.0000000000000000 4.000000 -0.6536436208636119 5.000000 0.2836621854632262 COS_DEGREE_VALUES_TEST: COS_DEGREE_VALUES stores values of the cosine function. X FX -5.000000 0.9961946980917455 0.000000 1.0000000000000000 1.000000 0.9998476951563913 2.000000 0.9993908270190958 3.000000 0.9986295347545738 4.000000 0.9975640502598242 5.000000 0.9961946980917455 10.000000 0.9848077530122080 15.000000 0.9659258262890683 30.000000 0.8660254037844386 45.000000 0.7071067811865476 60.000000 0.5000000000000000 75.000000 0.2588190451025207 85.000000 0.0871557427476582 86.000000 0.0697564737441253 87.000000 0.0523359562429438 88.000000 0.0348994967025010 89.000000 0.0174524064372835 90.000000 0.0000000000000000 91.000000 -0.0174524064372835 105.000000 -0.2588190451025207 180.000000 -1.0000000000000000 COS_POWER_INT_VALUES_TEST: COS_POWER_INT_VALUES returns values of the N-th power of the cosine function. A B N FX 0.000000 3.141593 0 3.1415926535897931 0.000000 3.141593 1 0.0000000000000000 0.000000 3.141593 2 1.5707963267948970 0.000000 3.141593 3 0.0000000000000000 0.000000 3.141593 4 1.1780972450961720 0.000000 3.141593 5 0.0000000000000000 0.000000 3.141593 6 0.9817477042468103 0.000000 3.141593 7 0.0000000000000000 0.000000 3.141593 8 0.8590292412159591 0.000000 3.141593 9 0.0000000000000000 0.000000 3.141593 10 0.7731263170943632 COSH_VALUES_TEST: COSH_VALUES stores values of the hyperbolic cosine function. X FX -5.000000 74.2099485247878476 -1.000000 1.5430806348152437 0.000000 1.0000000000000000 0.100000 1.0050041680558035 0.200000 1.0200667556190759 0.300000 1.0453385141288605 0.400000 1.0810723718384547 0.500000 1.1276259652063807 0.600000 1.1854652182422678 0.700000 1.2551690056309430 0.800000 1.3374349463048445 0.900000 1.4330863854487743 1.000000 1.5430806348152437 2.000000 3.7621956910836314 3.000000 10.0676619957777653 4.000000 27.3082328360164865 5.000000 74.2099485247878476 10.000000 11013.2329201033226127 COT_VALUES_TEST: COT_VALUES stores values of the cotangent function. X FX 0.083333 11.9722093536286618 0.261799 3.7320508075688772 0.500000 1.8304877217124520 0.523599 1.7320508075688772 0.785398 1.0000000000000000 1.000000 0.6420926159343308 1.047198 0.5773502691896257 1.308997 0.2679491924311227 1.570796 0.0000000000000000 1.439897 0.1316524975873959 1.505346 0.0655434628152382 2.000000 -0.4576575543602858 3.000000 -7.0152525514345339 4.000000 0.8636911544506166 5.000000 -0.2958129155327455 CP_VALUES_TEST: CP_VALUES stores values of the specific heat CP as a function of temperature and pressure. T P CP(T,P) 0.000000 1.000000 4.2279999999999998 100.000000 1.000000 2.0419999999999998 200.000000 1.000000 1.9750000000000001 300.000000 1.000000 2.0129999999999999 350.000000 1.000000 2.0400000000000000 400.000000 1.000000 2.0699999999999998 500.000000 1.000000 2.1349999999999998 600.000000 1.000000 2.2029999999999998 850.000000 1.000000 2.3780000000000001 1100.000000 1.000000 2.5409999999999999 1600.000000 1.000000 2.7919999999999998 2000.000000 1.000000 2.9310000000000000 0.000000 5.000000 4.2260000000000000 0.000000 10.000000 4.2229999999999999 0.000000 50.000000 4.2020000000000000 0.000000 100.000000 4.1769999999999996 0.000000 200.000000 4.1299999999999999 0.000000 300.000000 4.0890000000000004 0.000000 400.000000 4.0529999999999999 0.000000 500.000000 4.0209999999999999 0.000000 1000.000000 3.9089999999999998 0.000000 1500.000000 3.8439999999999999 0.000000 2000.000000 3.7860000000000000 0.000000 5000.000000 2.8900000000000001 DATENUM_VALUES_TEST: DATENUM_VALUES stores values of the MATLAB DATENUM for a given Y/M/D date. Y M D Date_Num 0 1 1 1 1 1 1 367 100 1 1 36526 1000 1 1 365244 1939 8 17 708434 1944 9 9 710284 1952 3 10 713023 1966 5 12 718199 1980 1 6 723186 1996 2 25 729080 2000 1 1 730486 DAWSON_VALUES_TEST: DAWSON_VALUES stores values of Dawson's Integral function. X DAWSON(X) 0.000000 0.0000000000000000 0.100000 0.0993359923978529 0.200000 0.1947510333680280 0.300000 0.2826316650213119 0.400000 0.3599434819348881 0.500000 0.4244363835020223 0.600000 0.4747632036629779 0.700000 0.5105040575592318 0.800000 0.5321017070563654 0.900000 0.5407243187262987 1.000000 0.5380795069127684 1.100000 0.5262066799705525 1.200000 0.5072734964077396 1.300000 0.4833975173848241 1.400000 0.4565072375268973 1.500000 0.4282490710853986 1.600000 0.3999398943230814 1.700000 0.3725593489740788 1.800000 0.3467727691148722 1.900000 0.3229743193228178 2.000000 0.3013403889237920 DEBYE1_VALUES_TEST: DEBYE1_VALUES stores values of the Debye function of order 1. X FX 0.001953 0.9995118247138088 0.031250 0.9922146264712060 0.125000 0.9691839599789531 0.500000 0.8819271567906055 1.000000 0.7775046341122482 1.500000 0.6861453107894020 2.000000 0.6069472846098101 2.500000 0.5387895690778559 3.000000 0.4804352195730429 4.000000 0.3881480212979379 4.250000 0.3693080282924253 5.000000 0.3208761977001461 5.500000 0.2942399662315425 6.000000 0.2712604667850219 8.000000 0.2052393031022150 10.000000 0.1644434656799460 15.000000 0.1096619448273582 20.000000 0.0822467011782000 30.000000 0.0548311355615109 50.000000 0.0328986813369645 DEBYE2_VALUES_TEST: DEBYE2_VALUES stores values of the Debye function of order 2. X FX 0.001953 0.9993491172790460 0.031250 0.9896240229959918 0.125000 0.9589842620034599 0.500000 0.8437211933472536 1.000000 0.7078784756278292 1.500000 0.5914963722567128 2.000000 0.4930826439905319 2.500000 0.4107941357974967 3.000000 0.3426139606078635 4.000000 0.2405536875212790 4.250000 0.2208277006120231 5.000000 0.1723291593901414 5.500000 0.1472434673873018 6.000000 0.1266691904671579 8.000000 0.0742688059548628 10.000000 0.0479714980201219 15.000000 0.0213692016836584 20.000000 0.0120205644764464 30.000000 0.0053424751249537 50.000000 0.0019232910450554 DEBYE3_VALUES_TEST: DEBYE3_VALUES stores values of the Debye function of order 3. X FX 0.001953 0.9992677688598546 0.031250 0.9883300775573470 0.125000 0.9539061047202351 0.500000 0.8249629689762337 1.000000 0.6744155640778147 1.500000 0.5471066514128629 2.000000 0.4411284737276242 2.500000 0.3541360348104239 3.000000 0.2835798281434225 4.000000 0.1817369138217748 4.250000 0.1627792438511244 5.000000 0.1175974117999340 5.500000 0.0952408027231589 6.000000 0.0775813247337630 8.000000 0.0365602956731948 10.000000 0.0192957656903455 15.000000 0.0057712632276189 20.000000 0.0024352200674805 30.000000 0.0007215488221634 50.000000 0.0001558545456544 DEBYE4_VALUES_TEST: DEBYE4_VALUES stores values of the Debye function of order 4. X FX 0.001953 0.9992189619276157 0.031250 0.9875542528099607 0.125000 0.9508678860638974 0.500000 0.8138456917203404 1.000000 0.6548740688867369 1.500000 0.5216283096487871 2.000000 0.4118927367178853 2.500000 0.3229543485870731 3.000000 0.2518786364288331 4.000000 0.1518546125867202 4.250000 0.1337266114592141 5.000000 0.0914713776644812 5.500000 0.0712278281974625 6.000000 0.0556765478227389 8.000000 0.0219675665255750 10.000000 0.0096736755602712 15.000000 0.0019646978158352 20.000000 0.0006221464862397 30.000000 0.0001228951409208 50.000000 0.0000159272103190 DEDEKIND_SUM_VALUES_TEST: DEDEKIND_SUM_VALUES stores values of the Dedekind sum: (N/D) = Dedekind_Sum ( P, Q ). P Q N D 1 1 0 1 1 2 0 1 1 3 1 18 1 4 1 8 1 5 1 5 1 6 5 18 1 7 5 14 1 8 7 16 1 9 14 27 1 10 3 5 1 11 15 22 1 12 55 72 1 13 11 13 1 14 13 14 1 15 91 90 1 16 35 32 1 17 20 17 1 18 34 27 1 19 51 38 1 20 57 40 2 1 0 1 2 3 -1 18 2 5 0 1 2 7 1 14 2 9 4 27 2 11 5 22 2 13 4 13 2 15 7 18 2 17 8 17 2 19 21 38 3 1 0 1 3 2 0 1 3 4 -1 8 3 5 0 1 3 7 -1 14 3 8 1 16 3 10 0 1 3 11 3 22 3 13 1 13 3 14 3 14 3 16 5 32 3 17 5 17 3 19 9 38 3 20 3 8 4 1 0 1 4 3 1 18 4 5 -1 5 4 7 1 14 4 9 -4 27 4 11 3 22 4 13 -1 13 4 15 19 90 4 17 0 1 4 19 11 38 5 1 0 1 5 2 0 1 5 3 -1 18 5 4 1 8 5 6 -5 18 5 7 -1 14 5 8 -1 16 5 9 4 27 5 11 -5 22 5 12 -1 72 5 13 0 1 5 14 3 14 5 16 -5 32 5 17 1 17 5 18 2 27 5 19 11 38 6 1 0 1 6 5 1 5 6 7 -5 14 6 11 5 22 6 13 -4 13 6 17 5 17 6 19 -9 38 7 1 0 1 7 2 0 1 7 3 1 18 7 4 -1 8 7 5 0 1 7 6 5 18 7 8 -7 16 7 9 -4 27 7 10 0 1 7 11 -3 22 7 12 1 72 7 13 4 13 7 15 -7 18 7 16 -3 32 7 17 1 17 7 18 -2 27 7 19 3 38 7 20 3 8 DIELECTRIC_VALUES_TEST: DIELECTRIC_VALUES stores values of the dielectric function. T P EPS(T,P) 0.000000 100.000000 88.2900000000000063 0.000000 500.000000 90.0699999999999932 0.000000 1000.000000 92.0199999999999960 0.000000 2000.000000 95.1400000000000006 0.000000 5000.000000 100.7699999999999960 25.000000 100.000000 78.8499999999999943 50.000000 100.000000 70.2699999999999960 75.000000 100.000000 62.6000000000000014 100.000000 100.000000 55.7800000000000011 150.000000 100.000000 44.3100000000000023 200.000000 100.000000 35.1099999999999994 300.000000 100.000000 20.3999999999999986 400.000000 100.000000 1.1699999999999999 500.000000 100.000000 1.1100000000000001 600.000000 100.000000 1.0800000000000001 DILOGARITHM_VALUES_TEST: DILOGARITHM_VALUES stores values of the dilogarithm function. X DILOGARITHM(X) 0.000000 0.0000000000000000 0.050000 0.0506392924644960 0.100000 0.1026177910993911 0.150000 0.1560350339454831 0.200000 0.2110037754397048 0.250000 0.2676526390827326 0.300000 0.3261295100754761 0.350000 0.3866059411605865 0.400000 0.4492829744712817 0.450000 0.5143989891542119 0.500000 0.5822405264650125 0.550000 0.6531576315069018 0.600000 0.7275863077163334 0.650000 0.8060826895177240 0.700000 0.8893776242860387 0.750000 0.9784693929303061 0.800000 1.0747946000082480 0.850000 1.1805811238302550 0.900000 1.2997147230049590 0.950000 1.4406337969700389 1.000000 1.6449340668482260 E1_VALUES_TEST: E1_VALUES stores values of the exponential integral function E1(X). X E1(X) 0.500000 0.5597735947761608 0.600000 0.4543795031894021 0.700000 0.3737688432335091 0.800000 0.3105965785455430 0.900000 0.2601839393259996 1.000000 0.2193839343955203 1.100000 0.1859909045360402 1.200000 0.1584084368514626 1.300000 0.1354509578491291 1.400000 0.1162193125713579 1.500000 0.1000195824066327 1.600000 0.0863083336975398 1.700000 0.0746546444012531 1.800000 0.0647131293638689 1.900000 0.0562043781745349 2.000000 0.0489005107080611 EASTER_GREGORIAN_VALUES_TEST: EASTER_GREGORIAN_VALUES stores values of the date of Easter in the Gregorian calendar. D M Y 30 3 1997 12 4 1998 4 4 1999 23 4 2000 15 4 2001 31 3 2002 20 4 2003 11 4 2004 27 3 2005 16 4 2006 EASTER_JULIAN_VALUES_TEST: EASTER_JULIAN_VALUES stores values of the date of Easter in the Julian calendar. D M Y 27 4 1997 19 4 1998 11 4 1999 30 4 2000 15 4 2001 5 5 2002 27 4 2003 11 4 2004 1 5 2005 23 4 2006 EI_VALUES_TEST: EI_VALUES stores values of the exponential integral function EI(X). X EI(X) 0.500000 0.4542199048631736 0.600000 0.7698812899373594 0.700000 1.0649071946242910 0.800000 1.3473965482123260 0.900000 1.6228117136968669 1.000000 1.8951178163559370 1.100000 2.1673782795634029 1.200000 2.4420922851926519 1.300000 2.7213988802320239 1.400000 3.0072074641506461 1.500000 3.3012854491297978 1.600000 3.6053199490194690 1.700000 3.9209632013549038 1.800000 4.2498675574879341 1.900000 4.5937136869535848 2.000000 4.9542343560018898 ELLIPTIC_EA_VALUES_TEST: ELLIPTIC_EA_VALUES stores values of the complete elliptic integral of the second kind, with parameter angle A in degrees. A E(A) 0.000000 1.5707963267948970 5.000000 1.5678090739776220 10.000000 1.5588871966015960 15.000000 1.5441504969146731 20.000000 1.5237992052597740 25.000000 1.4981149284221160 30.000000 1.4674622093394269 35.000000 1.4322909693067560 40.000000 1.3931402485238120 45.000000 1.3506438810476760 50.000000 1.3055390942977940 55.000000 1.2586796247799970 60.000000 1.2110560275684590 65.000000 1.1638279644931391 70.000000 1.1183777379698641 75.000000 1.0764051130764030 80.000000 1.0401143957060099 85.000000 1.0126635062343960 90.000000 1.0000000000000000 ELLIPTIC_EK_VALUES_TEST: ELLIPTIC_EK_VALUES stores values of the complete elliptic integral of the second kind, with parameter modulus K. K E(K) 0.000000 1.5707963267948970 0.223607 1.5509733517804720 0.316228 1.5307576368977629 0.387298 1.5101218320928189 0.447214 1.4890350580958529 0.500000 1.4674622093394269 0.547723 1.4453630644126649 0.591608 1.4226911334908789 0.632456 1.3993921388974320 0.670820 1.3754019718711159 0.707107 1.3506438810476760 0.741620 1.3250244979582300 0.774597 1.2984280350469131 0.806226 1.2707074796501490 0.836660 1.2416705679458231 0.866025 1.2110560275684590 0.894427 1.1784899243278391 0.921954 1.1433957918831661 0.948683 1.1047747327040729 0.974679 1.0604737277662779 1.000000 1.0000000000000000 ELLIPTIC_EM_VALUES_TEST: ELLIPTIC_EM_VALUES stores values of the complete elliptic integral of the second kind, with parameter modulus M. M E(M) 0.000000 1.5707963267948970 0.050000 1.5509733517804720 0.100000 1.5307576368977629 0.150000 1.5101218320928189 0.200000 1.4890350580958529 0.250000 1.4674622093394269 0.300000 1.4453630644126649 0.350000 1.4226911334908789 0.400000 1.3993921388974320 0.450000 1.3754019718711159 0.500000 1.3506438810476760 0.550000 1.3250244979582300 0.600000 1.2984280350469131 0.650000 1.2707074796501490 0.700000 1.2416705679458231 0.750000 1.2110560275684590 0.800000 1.1784899243278391 0.850000 1.1433957918831661 0.900000 1.1047747327040729 0.950000 1.0604737277662779 1.000000 1.0000000000000000 ELLIPTIC_FA_VALUES_TEST: ELLIPTIC_FA_VALUES stores values of the complete elliptic integral of the first kind, with parameter angle A in degrees. A F(A) 0.000000 1.5707963267948970 5.000000 1.5737921309247680 10.000000 1.5828428043383509 15.000000 1.5981420021125401 20.000000 1.6200258991242040 25.000000 1.6489952184785299 30.000000 1.6857503548125961 35.000000 1.7312451756570579 40.000000 1.7867691348850210 45.000000 1.8540746773013721 50.000000 1.9355810960047219 55.000000 2.0347153121857908 60.000000 2.1565156474996430 65.000000 2.3087867981671959 70.000000 2.5045500790016342 75.000000 2.7680631453687679 80.000000 3.1533852518878391 85.000000 3.8317419997841462 ELLIPTIC_FK_VALUES_TEST: ELLIPTIC_FK_VALUES stores values of the complete elliptic integral of the first kind, with parameter K. K F(K) 0.000000 1.5707963267948970 0.223607 1.5910034537907920 0.316228 1.6124413487202189 0.387298 1.6352567322645799 0.447214 1.6596235986105281 0.500000 1.6857503548125961 0.547723 1.7138894481787910 0.591608 1.7443505972256130 0.632456 1.7775193714912529 0.670820 1.8138839368169830 0.707107 1.8540746773013721 0.741620 1.8989249102715540 0.774597 1.9495677498060260 0.806226 2.0075983984243759 0.836660 2.0753631352924691 0.866025 2.1565156474996430 0.894427 2.2572053268208538 0.921954 2.3890164863255801 0.948683 2.5780921133481729 0.974679 2.9083372484445520 ELLIPTIC_FM_VALUES_TEST: ELLIPTIC_FM_VALUES stores values of the complete elliptic integral of the first kind, with parameter modulus M. M F(M) 0.000000 1.5707963267948970 0.050000 1.5910034537907920 0.100000 1.6124413487202189 0.150000 1.6352567322645799 0.200000 1.6596235986105281 0.250000 1.6857503548125961 0.300000 1.7138894481787910 0.350000 1.7443505972256130 0.400000 1.7775193714912529 0.450000 1.8138839368169830 0.500000 1.8540746773013721 0.550000 1.8989249102715540 0.600000 1.9495677498060260 0.650000 2.0075983984243759 0.700000 2.0753631352924691 0.750000 2.1565156474996430 0.800000 2.2572053268208538 0.850000 2.3890164863255801 0.900000 2.5780921133481729 0.950000 2.9083372484445520 ELLIPTIC_INC_EA_VALUES_TEST: ELLIPTIC_INC_EA_VALUES stores values of the incomplete elliptic integral of the second kind, with parameters PHI, A. PHI A E(PHI,A) 0.343091 123.082123 0.3384181367348019 1.302990 11.269317 1.2929246245095061 0.652363 -94.888065 0.6074183768796306 0.404602 -99.714079 0.3939726730783567 0.068846 57.058810 0.0688081409708980 0.096961 -19.713633 0.0969436473376824 0.630370 56.312303 0.6025937791452033 1.252375 -91.556053 0.9500549494837583 1.409796 -27.006546 1.3427833721404860 0.148511 -169.229373 0.1484915631401388 1.349466 61.968596 1.0854328870509260 0.193371 -158.732440 0.1932136916085597 0.408883 105.088396 0.3983689593057807 0.178543 -48.958839 0.1780054133336934 1.292588 -42.585688 1.1645252702735360 1.087096 11.656033 1.0801670475418450 1.352795 -8.398114 1.3466849638303120 1.432530 17.693622 1.4021002726855041 0.296809 73.880342 0.2928091845544553 0.623588 -69.824923 0.5889342583405707 ELLIPTIC_INC_EK_VALUES_TEST: ELLIPTIC_INC_EK_VALUES stores values of the incomplete elliptic integral of the second kind, with parameters PHI, K. PHI K E(PHI,K) 0.343091 2.712953 0.2852345328295404 1.302990 0.127952 1.2986902255679209 0.652363 -1.429438 0.5508100202571943 0.404602 -1.981659 0.3575401358115371 0.068846 3.894802 0.0680130780550745 0.096961 -1.042486 0.0967958498023184 0.630370 0.864114 0.6003112504412838 1.252375 -1.049058 0.8996717721794724 1.409796 -0.302406 1.3807152614538749 0.148511 -6.574289 0.1191644625202453 1.349466 0.698740 1.1969948381715569 0.193371 -5.125586 0.1536260979667945 0.408883 2.074948 0.3546768920544152 0.178543 -1.670886 0.1758756066650882 1.292588 -0.484360 1.2298191094105690 1.087096 0.139306 1.0838106611433700 1.352795 -0.094653 1.3502337815737799 1.432530 0.197721 1.4197758847092179 0.296809 1.788160 0.2824895528020034 0.623588 -1.077781 0.5770427720982867 ELLIPTIC_INC_EM_VALUES_TEST: ELLIPTIC_INC_EM_VALUES stores values of the incomplete elliptic integral of the second kind, with parameters PHI, M. PHI M E(PHI,M) 8.450690 8.450690 0.2732317284159052 0.603988 0.603988 1.1247497250997811 0.179413 0.179413 0.6446601913679151 0.709569 0.709569 0.3968902354370061 133.964339 133.964339 0.0606396079994467 47.966214 47.966214 0.0890941157794873 2.172071 2.172071 0.5324020148020150 0.002038 0.002038 1.2518886406602650 0.360004 0.360004 1.2889711619162600 0.621954 0.621954 0.1481718153599732 0.883422 0.883422 1.0380901856399130 0.203429 0.203429 0.1931275771541276 5.772526 5.772526 0.3304419611986801 11.148539 11.148539 0.1673947960639630 0.288924 0.288924 1.2145011753247359 0.716662 0.716662 0.9516560179840655 0.476062 0.476062 1.2036829595261760 0.609495 0.609495 1.2064263261854189 8.902277 8.902277 0.2522791382096692 0.543444 0.543444 0.6026499038720986 ELLIPTIC_INC_FA_VALUES_TEST: ELLIPTIC_INC_FA_VALUES stores values of the incomplete elliptic integral of the first kind, with parameters PHI, A. PHI A F(PHI,A) 0.343091 123.082123 0.3478806460316299 1.302990 11.269317 1.3131805770095839 0.652363 -94.888065 0.7037956689264326 0.404602 -99.714079 0.4157626844675118 0.068846 57.058810 0.0688847548328514 0.096961 -19.713633 0.0969781675484583 0.630370 56.312303 0.6605394722518515 1.252375 -91.556053 1.8275834603675101 1.409796 -27.006546 1.4822587833924870 0.148511 -169.229373 0.1485295339221232 1.349466 61.968596 1.7538000627014940 0.193371 -158.732440 0.1935288964653510 0.408883 105.088396 0.4199100508706138 0.178543 -48.958839 0.1790836490491233 1.292588 -42.585688 1.4460488322797631 1.087096 11.656033 1.0940976521009840 1.352795 -8.398114 1.3589479084270351 1.432530 17.693622 1.4640007823153800 0.296809 73.880342 0.3009092014525799 0.623588 -69.824923 0.6621341112075102 ELLIPTIC_INC_FK_VALUES_TEST: ELLIPTIC_INC_FK_VALUES stores values of the incomplete elliptic integral of the first kind, with parameters PHI, K. PHI K F(PHI,K) 0.343091 2.712953 0.4340870330108736 1.302990 0.127952 1.3073125113981141 0.652363 -1.429438 0.8005154258533936 0.404602 -1.981659 0.4656721451084328 0.068846 3.894802 0.0696984961344177 0.096961 -1.042486 0.0971264670875049 0.630370 0.864114 0.6632598061016007 1.252375 -1.049058 2.2308677858579000 1.409796 -0.302406 1.4398462828880190 0.148511 -6.574289 0.2043389243773096 1.349466 0.698740 1.5371835748817710 0.193371 -5.125586 0.2749229901565622 0.408883 2.074948 0.4828388342828284 0.178543 -1.670886 0.1812848567886627 1.292588 -0.484360 1.3607295223418410 1.087096 0.139306 1.0903968091202700 1.352795 -0.094653 1.3553630515818080 1.432530 0.197721 1.4454628197324411 0.296809 1.788160 0.3125355489354676 0.623588 -1.077781 0.6775731623807174 ELLIPTIC_INC_FM_VALUES_TEST: ELLIPTIC_INC_FM_VALUES stores values of the incomplete elliptic integral of the first kind, with parameters PHI, M. PHI M F(PHI,M) 0.343091 8.450690 0.4804314075855023 1.302990 0.603988 1.5356349810920249 0.652363 0.179413 0.6602285297476601 0.404602 0.709569 0.4125884303785135 0.068846 133.964339 0.0796456600715538 0.096961 47.966214 0.1062834070535258 0.630370 2.172071 0.7733990864393913 1.252375 0.002038 1.2528624998922280 1.409796 0.360004 1.5499886866115320 0.148511 0.621954 0.1488506735822822 1.349466 0.883422 1.8922299007996619 0.193371 0.203429 0.1936153327753556 0.408883 5.772526 0.5481932935424454 0.178543 11.148539 0.1911795073571756 1.292588 0.288924 1.3792250693497561 1.087096 0.716662 1.2612824533314020 1.352795 0.476062 1.5352398385253780 1.432530 0.609495 1.7397824181560710 0.296809 8.902277 0.3616930047198503 0.623588 0.543444 0.6458627645916422 ELLIPTIC_INC_PIA_VALUES_TEST: ELLIPTIC_INC_PIA_VALUES stores values of the incomplete elliptic integral of the third kind, with parameters PHI, N and A. PHI N A Pi(PHI,N,A) 0.343091 8.064681 88.878225 0.7099335174334724 0.882309 -0.284059 -86.552087 0.9601963779142505 0.404602 -5.034023 -116.619570 0.3362852532098376 0.995831 -1.244606 -9.742878 0.7785343427543768 0.630370 1.465982 65.734809 0.8578897552144780 0.002888 95338.128573 -115.038772 0.0046307723449318 0.148511 -44.431306 124.942118 0.1173842687902911 1.320800 -0.802937 -89.787044 1.5057880706602671 0.408883 5.218883 -98.426738 0.7213264194624553 0.552337 2.345822 -53.749362 0.8073261799642218 1.087096 0.157358 68.280476 1.4028538111108380 0.712818 1.926593 20.821747 1.2592453314745129 0.296809 6.113983 -29.104236 0.3779079263971614 0.291091 1.805711 -37.801767 0.3088493910496766 0.969503 -0.407285 -55.811734 0.9782829177005183 1.122289 -0.941640 -37.665946 0.9430491574504173 1.295912 0.700966 -80.094082 3.3207962773841548 1.116491 -1.019831 52.238065 0.9730988737054799 1.170719 -0.451080 74.309452 1.3019880949537890 1.199361 0.602882 -17.229207 1.6455836044525900 ELLIPTIC_INC_PIK_VALUES_TEST: ELLIPTIC_INC_PIK_VALUES stores values of the incomplete elliptic integral of the third kind, with parameters PHI, N and K. PHI N K Pi(PHI,N,K) 0.343091 8.064681 1.959037 0.7982975462595892 0.882309 -0.284059 -1.123742 1.0240221347260361 0.404602 -5.034023 -2.317629 0.4015812085264200 0.995831 -1.244606 -0.120258 0.7772649487439858 0.630370 1.465982 1.008703 0.8737159913132074 0.002888 95338.128573 -103.367749 0.0047333342976913 0.148511 -44.431306 4.853800 0.1280656893638068 1.320800 -0.802937 -1.016577 1.5943760375125640 0.408883 5.218883 -1.943415 0.8521145133671923 0.552337 2.345822 -0.887659 0.8154325229803082 1.087096 0.157358 0.816049 1.3159451407542699 0.712818 1.926593 0.299455 1.2539462314842400 0.296809 6.113983 -0.704423 0.3796503567258643 0.291091 1.805711 -0.926652 0.3111034454739552 0.969503 -0.407285 -0.696261 0.9442477901112342 1.122289 -0.941640 -0.445393 0.9153111661980959 1.295912 0.700966 -0.910458 2.8420806443283930 1.116491 -1.019831 0.618750 0.9263253777034376 1.170719 -0.451080 0.867231 1.2123960187576239 1.199361 0.602882 -0.199677 1.6280835727104710 ELLIPTIC_INC_PIM_VALUES_TEST: ELLIPTIC_INC_PIM_VALUES stores values of the incomplete elliptic integral of the third kind, with parameters PHI, N and M. PHI N M Pi(PHI,N,M) 0.343091 8.064681 7.330123 1.0469349800784999 0.882309 -0.284059 0.110881 0.8421144481406690 0.404602 -5.034023 0.282836 0.3321642201520043 0.995831 -1.244606 0.638300 0.8483033529960849 0.630370 1.465982 2.294719 1.0557538176567720 0.002888 95338.128573 42062.553298 0.0051088961442656 0.148511 -44.431306 39.239434 0.1426848042785896 1.320800 -0.802937 0.008002 1.0313509582064240 0.408883 5.218883 0.719058 0.7131013701418496 0.552337 2.345822 0.970377 0.8268044665355507 1.087096 0.157358 1.098881 1.5763286789601501 0.712818 1.926593 1.398067 1.5428171208572110 0.296809 6.113983 4.641022 0.4144629799126912 0.291091 1.805711 4.455969 0.3313231611366746 0.969503 -0.407285 0.313145 0.9195822851915201 1.122289 -0.941640 0.368644 0.9422320754002217 1.295912 0.700966 0.066782 2.0365990028158589 1.116491 -1.019831 0.963554 1.0767992314998820 1.170719 -0.451080 1.060209 1.4160844629578520 1.199361 0.602882 0.468716 1.8241249223108911 ELLIPTIC_PIA_VALUES_TEST: ELLIPTIC_PIA_VALUES stores values of the complete elliptic integral of the third kind, with parameter angle A in degrees. N A Pi(N,A) -10.000000 30.000000 0.4892245275965397 -10.000000 45.000000 0.5106765677902629 -10.000000 60.000000 0.5460409271920561 -10.000000 77.079034 0.6237325893535237 -3.000000 30.000000 0.8230455426606750 -3.000000 45.000000 0.8760028274011437 -3.000000 60.000000 0.9660073560143946 -3.000000 77.079034 1.1719523914817980 -1.000000 30.000000 1.1774468430005660 -1.000000 45.000000 1.2731273667496821 -1.000000 60.000000 1.4400343186575510 -1.000000 77.079034 1.8364721723025910 0.000000 30.000000 1.6857503548125961 0.000000 45.000000 1.8540746773013721 0.000000 60.000000 2.1565156474996430 0.000000 77.079034 2.9083372484445520 0.500000 30.000000 2.4136715042011949 0.500000 45.000000 2.7012877620953510 0.500000 60.000000 3.2347734712494649 0.500000 77.079034 4.6333081472798909 ELLIPTIC_PIK_VALUES_TEST: ELLIPTIC_PIK_VALUES stores values of the complete elliptic integral of the third kind, with parameter K. N K Pi(N,K) -10.000000 0.500000 0.4892245275965397 -10.000000 0.707107 0.5106765677902629 -10.000000 0.866025 0.5460409271920561 -10.000000 0.974679 0.6237325893535237 -3.000000 0.500000 0.8230455426606750 -3.000000 0.707107 0.8760028274011437 -3.000000 0.866025 0.9660073560143946 -3.000000 0.974679 1.1719523914817980 -1.000000 0.500000 1.1774468430005660 -1.000000 0.707107 1.2731273667496821 -1.000000 0.866025 1.4400343186575510 -1.000000 0.974679 1.8364721723025910 0.000000 0.500000 1.6857503548125961 0.000000 0.707107 1.8540746773013721 0.000000 0.866025 2.1565156474996430 0.000000 0.974679 2.9083372484445520 0.500000 0.500000 2.4136715042011949 0.500000 0.707107 2.7012877620953510 0.500000 0.866025 3.2347734712494649 0.500000 0.974679 4.6333081472798909 ELLIPTIC_PIM_VALUES_TEST: ELLIPTIC_PIM_VALUES stores values of the complete elliptic integral of the third kind, with parameter modulus M. N M Pi(N,M) -10.000000 0.250000 0.4892245275965397 -10.000000 0.500000 0.5106765677902629 -10.000000 0.750000 0.5460409271920561 -10.000000 0.950000 0.6237325893535237 -3.000000 0.250000 0.8230455426606750 -3.000000 0.500000 0.8760028274011437 -3.000000 0.750000 0.9660073560143946 -3.000000 0.950000 1.1719523914817980 -1.000000 0.250000 1.1774468430005660 -1.000000 0.500000 1.2731273667496821 -1.000000 0.750000 1.4400343186575510 -1.000000 0.950000 1.8364721723025910 0.000000 0.250000 1.6857503548125961 0.000000 0.500000 1.8540746773013721 0.000000 0.750000 2.1565156474996430 0.000000 0.950000 2.9083372484445520 0.500000 0.250000 2.4136715042011949 0.500000 0.500000 2.7012877620953510 0.500000 0.750000 3.2347734712494649 0.500000 0.950000 4.6333081472798909 ERF_VALUES_TEST: ERF_VALUES stores values of the error function ERF(X). X ERF(X) 0.000000 0.0000000000000000 0.100000 0.1124629160182849 0.200000 0.2227025892104785 0.300000 0.3286267594591274 0.400000 0.4283923550466685 0.500000 0.5204998778130465 0.600000 0.6038560908479259 0.700000 0.6778011938374185 0.800000 0.7421009647076605 0.900000 0.7969082124228321 1.000000 0.8427007929497149 1.100000 0.8802050695740817 1.200000 0.9103139782296354 1.300000 0.9340079449406524 1.400000 0.9522851197626488 1.500000 0.9661051464753106 1.600000 0.9763483833446440 1.700000 0.9837904585907746 1.800000 0.9890905016357306 1.900000 0.9927904292352575 2.000000 0.9953222650189527 ERFC_VALUES_TEST: ERFC_VALUES stores values of the complmementary error function ERFC(X). X ERFC(X) 0.000000 1.0000000000000000 0.200000 0.7772974107895215 0.400000 0.5716076449533315 0.600000 0.3961439091520741 0.800000 0.2578990352923395 1.000000 0.1572992070502851 1.200000 0.0896860217703646 1.400000 0.0477148802373512 1.600000 0.0236516166553560 1.800000 0.0109094983642693 2.000000 0.0046777349810473 2.200000 0.0018628462979819 2.400000 0.0006885138966451 2.600000 0.0002360344165293 2.800000 0.0000750131946655 3.000000 0.0000220904969986 3.200000 0.0000060257611518 3.400000 0.0000015219933629 3.600000 0.0000003558629930 3.800000 0.0000000770039275 4.000000 0.0000000154172579 EULER_NUMBER_VALUES_TEST: EULER_NUMBER_VALUES returns values of the Euler numbers. N EULER_NUMBER(N) 0 1 1 0 2 -1 4 5 6 -61 8 1385 10 -50521 12 2702765 EULER_POLY_VALUES_TEST: EULER_POLY_VALUES stores values of the Euler polynomials. N X FX 0 0.200000 1.0000000000000000 1 0.200000 -0.3000000000000000 2 0.200000 -0.1600000000000000 3 0.200000 0.1980000000000000 4 0.200000 0.1856000000000000 5 0.200000 -0.4036800000000000 6 0.200000 -0.5608960000000000 7 0.200000 1.7187888000000000 8 0.200000 3.1804313600000000 9 0.200000 -12.5394670080000008 10 0.200000 -28.9999384575999990 5 -0.500000 -0.0625000000000000 5 -0.400000 -0.1742400000000000 5 -0.300000 -0.2976800000000000 5 -0.200000 -0.4043200000000000 5 -0.100000 -0.4752600000000000 5 0.000000 -0.5000000000000000 5 0.100000 -0.4752400000000000 5 0.200000 -0.4036800000000000 5 0.300000 -0.2928200000000000 5 0.400000 -0.1537600000000000 5 0.500000 0.0000000000000000 5 0.600000 0.1537600000000000 5 0.700000 0.2928200000000000 5 0.800000 0.4036800000000000 5 0.900000 0.4752400000000000 5 1.000000 0.5000000000000000 EXP_VALUES_TEST: EXP_VALUES stores values of the exponential function. X FX -10.000000 0.0000453999297625 -5.000000 0.0067379469990855 -1.000000 0.3678794411714423 0.000000 1.0000000000000000 0.000000 1.0000000099999999 0.000100 1.0001000050001667 0.001000 1.0010005001667084 0.010000 1.0100501670841679 0.100000 1.1051709180756477 0.200000 1.2214027581601699 0.300000 1.3498588075760032 0.400000 1.4918246976412703 0.500000 1.6487212707001282 0.600000 1.8221188003905089 0.700000 2.0137527074704766 0.800000 2.2255409284924674 0.900000 2.4596031111569499 1.000000 2.7182818284590451 2.000000 7.3890560989306504 3.141593 23.1406926327792704 5.000000 148.4131591025765999 10.000000 22026.4657948067178950 20.000000 485165195.4097902774810791 40.000000 235385266837020000.0000000000000000 EXP3_INT_VALUES_TEST: EXP3_INT_VALUES stores values of the EXP3 Integral function. X FX 0.001953 0.0019531249963620 0.007812 0.0078124990686776 0.031250 0.0312497615834997 0.125000 0.1249389988880308 0.500000 0.4849171431136397 1.000000 0.8075111821396714 1.250000 0.8688926541262327 1.500000 0.8886172223535717 1.875000 0.8928601850021818 2.000000 0.8929535142938763 2.125000 0.8929747911273784 2.250000 0.8929788057979812 2.500000 0.8929795031749662 2.750000 0.8929795115295190 3.000000 0.8929795115691812 3.125000 0.8929795115692474 3.250000 0.8929795115692492 3.500000 0.8929795115692493 3.750000 0.8929795115692493 4.000000 0.8929795115692493 EXPONENTIAL_01_PDF_VALUES_TEST: EXPONENTIAL_01_PDF_VALUES stores values of the standard exponential Probability Density Function. X PDF(X) 0.7013006334030669 0.4959398481993681 4.759746670799113 0.00856777959135697 4.062300786629853 0.01720937842266235 2.589324935217918 0.07507070056996956 1.784188948117787 0.1679332083261492 -0.1363469579618277 0 0.9166778581012469 0.399845179478639 0.1047623644285883 0.9005384971416223 -0.2589405122149109 0 2.986811417663269 0.05044803826563792 EXPONENTIAL_CDF_VALUES_TEST: EXPONENTIAL_CDF_VALUES stores values of the Exponential CDF. LAMBDA X FX 0.500000 1.000000 0.3934693402873666 0.500000 2.000000 0.6321205588285577 0.500000 3.000000 0.7768698398515702 0.500000 4.000000 0.8646647167633873 1.000000 2.000000 0.8646647167633873 2.000000 2.000000 0.9816843611112658 3.000000 2.000000 0.9975212478233336 4.000000 2.000000 0.9996645373720975 5.000000 2.000000 0.9999546000702375 EXPONENTIAL_PDF_VALUES_TEST: EXPONENTIAL_PDF_VALUES stores values of the Exponential PDF. BETA X FX 1.09209 9.55881 0.0001446999730194618 4.14755 5.57312 0.06289850821824726 2.07654 0.567799 0.3663607831924032 1.28789 1.01056 0.3542787877169571 0.219145 6.30305 1.472582451176006e-12 0.308636 4.44034 1.829637907028298e-06 2.00653 7.5222 0.01173398427218792 3.98643 -0.0814325 0 4.48752 3.4426 0.1034724689882351 0.472724 0.0375306 1.95394780436833 EXTREME_VALUES_CDF_VALUES_TEST: EXTREME_VALUES_CDF_VALUES stores values of the Extreme Values CDF. ALPHA BETA X FX 1.000000 0.500000 1.000000 0.3678794411714423 1.000000 0.500000 2.000000 0.8734230184931167 1.000000 0.500000 3.000000 0.9818510730616665 1.000000 0.500000 4.000000 0.9975243173927525 1.000000 2.000000 2.000000 0.5452392118926050 1.000000 3.000000 2.000000 0.4884435800065159 1.000000 4.000000 2.000000 0.4589560693076638 1.000000 5.000000 2.000000 0.4409910259429826 2.000000 2.000000 3.000000 0.5452392118926050 3.000000 2.000000 3.000000 0.3678794411714423 4.000000 2.000000 3.000000 0.1922956455479649 5.000000 2.000000 3.000000 0.0659880358453125 F_CDF_VALUES_TEST: F_CDF_VALUES stores values of the F cumulative density function. A B X F_CDF(A,B)(X) 1.000000 1.000000 1.000000 0.5000000000000000 1.000000 5.000000 0.528000 0.4999714850534485 5.000000 1.000000 1.890000 0.4996034370170990 1.000000 5.000000 1.690000 0.7496993658293228 2.000000 10.000000 1.600000 0.7504656462757382 4.000000 20.000000 1.470000 0.7514156325324275 1.000000 5.000000 4.060000 0.8999867031372156 6.000000 6.000000 3.050000 0.8997127554259698 8.000000 16.000000 2.090000 0.9002845660853669 1.000000 5.000000 6.610000 0.9500248817817623 3.000000 10.000000 3.710000 0.9500574946122442 6.000000 12.000000 3.000000 0.9501926400000000 1.000000 5.000000 10.010000 0.9750133887312993 1.000000 5.000000 16.260000 0.9900022327445249 1.000000 5.000000 22.780000 0.9949977837872073 1.000000 5.000000 47.180000 0.9989999621122122 2.000000 5.000000 1.000000 0.5687988496283078 3.000000 5.000000 1.000000 0.5351452100063649 4.000000 5.000000 1.000000 0.5143428032407864 5.000000 5.000000 1.000000 0.5000000000000000 F_NONCENTRAL_CDF_VALUES: F_NONCENTRAL_CDF_VALUES stores values of the F cumulative density function. A B LAMBDA X F_CDF(A,B)(X) 1 1 0.000000 1.000000 5.0000000000000000e-01 1 5 0.000000 1.000000 6.3678253235087745e-01 1 5 0.250000 1.000000 5.8409161163054824e-01 1 5 1.000000 0.500000 3.2344318723927878e-01 1 5 1.000000 1.000000 4.5011878798135502e-01 1 5 1.000000 2.000000 6.0788814411883119e-01 1 5 1.000000 3.000000 7.0592755514146055e-01 1 5 1.000000 4.000000 7.7217820032637274e-01 1 5 1.000000 5.000000 8.1910490176350725e-01 1 5 2.000000 1.000000 3.1703484307499652e-01 2 5 1.000000 1.000000 4.3272180084544709e-01 2 10 1.000000 1.000000 4.5026969157073271e-01 3 5 1.000000 1.000000 4.2618811865940959e-01 3 5 2.000000 1.000000 6.7536872063415443e-01 4 5 1.000000 1.000000 4.2291087788790049e-01 4 5 1.000000 2.000000 6.9276672612289381e-01 5 1 0.000000 1.000000 3.6321746764912261e-01 5 5 1.000000 1.000000 4.2100540126958652e-01 6 6 1.000000 1.000000 4.2666722588189271e-01 6 12 1.000000 1.000000 4.4640166005246440e-01 8 16 1.000000 2.000000 8.4458885795048266e-01 16 8 1.000000 2.000000 4.3393002733436042e-01 FRESNEL_COS_VALUES_TEST: FRESNEL_COS_VALUES stores values of the Fresnel cosine integral C(X). X C(X) 0.000000 0.0000000000000000 0.200000 0.1999210575944531 0.400000 0.3974807591723594 0.600000 0.5810954469916523 0.800000 0.7228441718963561 1.000000 0.7798934003768228 1.200000 0.7154377229230734 1.400000 0.5430957835462564 1.600000 0.3654616834404877 1.800000 0.3336329272215571 2.000000 0.4882534060753408 2.200000 0.6362860449033195 2.400000 0.5549614058564281 2.600000 0.3889374961919690 2.800000 0.4674916516989059 3.000000 0.6057207892976856 FRESNEL_SIN_VALUES_TEST: FRESNEL_SIN_VALUES stores values of the Fresnel sine integral S(X). X S(X) 0.000000 0.0000000000000000 0.200000 0.0041876091616568 0.400000 0.0333594326606132 0.600000 0.1105402073593870 0.800000 0.2493413930539178 1.000000 0.4382591473903548 1.200000 0.6234009185462497 1.400000 0.7135250773634121 1.600000 0.6388876835093809 1.800000 0.4509387692675831 2.000000 0.3434156783636982 2.200000 0.4557046121246569 2.400000 0.6196899649456836 2.600000 0.5499893231527195 2.800000 0.3915284435431718 3.000000 0.4963129989673750 FROBENIUS_NUMBER_DATA_VALUES_TEST: FROBENIUS_NUMBER_DATA_VALUES returns the corresponding coin denominations. Order = 2 2 5 Frobenius number = 3 Order = 2 3 17 Frobenius number = 31 Order = 2 4 19 Frobenius number = 53 Order = 2 5 13 Frobenius number = 47 Order = 2 12 11 Frobenius number = 109 Order = 2 99 100 Frobenius number = 9701 Order = 3 6 9 20 Frobenius number = 43 Order = 3 5 17 23 Frobenius number = 41 Order = 3 137 251 256 Frobenius number = 4948 Order = 4 31 41 47 61 Frobenius number = 240 Order = 4 271 277 281 283 Frobenius number = 13022 Order = 5 10 18 26 33 35 Frobenius number = 67 Order = 5 34 37 38 40 43 Frobenius number = 175 Order = 5 12223 12224 36674 61119 85569 Frobenius number = 89643481 Order = 6 1000 1476 3764 4864 4871 7773 Frobenius number = 47350 Order = 6 12228 36679 36682 46908 61139 73365 Frobenius number = 89716838 Order = 6 12137 36405 24269 36407 84545 60683 Frobenius number = 58925134 Order = 7 13211 13212 39638 66060 52864 79268 92482 Frobenius number = 104723595 Order = 8 13429 26850 26855 40280 40281 53711 53714 67141 Frobenius number = 45094583 FROBENIUS_NUMBER_ORDER_VALUES_TEST: FROBENIUS_NUMBER_ORDER_VALUES returns the order for a Frobenius problem; Order = 2 2 5 Frobenius number = 3 Order = 2 3 17 Frobenius number = 31 Order = 2 4 19 Frobenius number = 53 Order = 2 5 13 Frobenius number = 47 Order = 2 12 11 Frobenius number = 109 Order = 2 99 100 Frobenius number = 9701 Order = 3 6 9 20 Frobenius number = 43 Order = 3 5 17 23 Frobenius number = 41 Order = 3 137 251 256 Frobenius number = 4948 Order = 4 31 41 47 61 Frobenius number = 240 Order = 4 271 277 281 283 Frobenius number = 13022 Order = 5 10 18 26 33 35 Frobenius number = 67 Order = 5 34 37 38 40 43 Frobenius number = 175 Order = 5 12223 12224 36674 61119 85569 Frobenius number = 89643481 Order = 6 1000 1476 3764 4864 4871 7773 Frobenius number = 47350 Order = 6 12228 36679 36682 46908 61139 73365 Frobenius number = 89716838 Order = 6 12137 36405 24269 36407 84545 60683 Frobenius number = 58925134 Order = 7 13211 13212 39638 66060 52864 79268 92482 Frobenius number = 104723595 Order = 8 13429 26850 26855 40280 40281 53711 53714 67141 Frobenius number = 45094583 FROBENIUS_NUMBER_ORDER2_VALUES_TEST: FROBENIUS_NUMBER_ORDER2_VALUES returns values of the Frobenius number of order 2. C1 C2 F(C1,C2) 2 5 3 3 17 31 4 19 53 5 13 47 12 11 109 99 100 9701 GAMMA_VALUES_TEST: GAMMA_VALUES stores values of the Gamma function. X GAMMA(X) -0.500000 -3.5449077018110322e+00 -0.010000 -1.0058719796441081e+02 0.010000 9.9432585119150602e+01 0.100000 9.5135076986687324e+00 0.200000 4.5908437119988026e+00 0.400000 2.2181595437576882e+00 0.500000 1.7724538509055161e+00 0.600000 1.4891922488128171e+00 0.800000 1.1642297137253030e+00 1.000000 1.0000000000000000e+00 1.100000 9.5135076986687317e-01 1.200000 9.1816874239976065e-01 1.300000 8.9747069630627718e-01 1.400000 8.8726381750307526e-01 1.500000 8.8622692545275805e-01 1.600000 8.9351534928769027e-01 1.700000 9.0863873285329044e-01 1.800000 9.3138377098024272e-01 1.900000 9.6176583190738740e-01 2.000000 1.0000000000000000e+00 3.000000 2.0000000000000000e+00 4.000000 6.0000000000000000e+00 10.000000 3.6288000000000000e+05 20.000000 1.2164510040883200e+17 30.000000 8.8417619937397019e+30 GAMMA_01_PDF_VALUES_TEST: GAMMA_01_PDF_VALUES stores values of the standard Gamma Probability Density Function. Alpha X PDF(X) 1.09209 9.54133 9.260811963612823e-05 4.14755 5.3978 0.1260335478747823 2.07654 0.194247 0.1363536772414351 1.28789 0.654546 0.5114450139194701 0.219145 6.15664 0.0001230139468263628 0.308636 4.22016 0.001870342832511005 2.00653 7.42407 0.004476000451227789 3.98643 -0.480697 0 4.48752 3.1829 0.2056668486524041 0.472724 -0.357023 0 GAMMA_CDF_VALUES_TEST: GAMMA_CDF_VALUES stores values of the Gamma CDF. MU SIGMA X FX 1.000000 0.500000 1.000000 0.8646647167633873 1.000000 0.500000 2.000000 0.9816843611112658 1.000000 0.500000 3.000000 0.9975212478233336 1.000000 0.500000 4.000000 0.9996645373720975 1.000000 2.000000 2.000000 0.6321205588285577 1.000000 3.000000 2.000000 0.4865828809674080 1.000000 4.000000 2.000000 0.3934693402873666 1.000000 5.000000 2.000000 0.3296799539643607 2.000000 2.000000 3.000000 0.4421745996289254 3.000000 2.000000 3.000000 0.1911531694619419 4.000000 2.000000 3.000000 0.0656424543784501 5.000000 2.000000 3.000000 0.0185759362221407 GAMMA_INC_VALUES_TEST: GAMMA_INC_VALUES stores values of the incomplete Gamma function. A X GAMMA_INC(A)(X) 0.100000 0.030000 2.4903028363005699 0.100000 0.300000 0.8718369702247978 0.100000 1.500000 0.1079213896175866 0.500000 0.075000 1.2381216858184170 0.500000 0.750000 0.3911298052193973 0.500000 3.500000 0.0144472209895253 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.0067379469990855 1.100000 0.100000 0.8827966752611692 1.100000 1.000000 0.3908330082003269 1.100000 5.000000 0.0080514566286210 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.0072950557244361 6.000000 2.500000 114.9574754165632982 6.000000 12.000000 2.4409235300314052 11.000000 16.000000 280854.6620274718152359 26.000000 25.000000 8576480283455533040533504.0000000000000000 41.000000 45.000000 208503134640336394638715847036779922009748406272.0000000000000000 GAMMA_INC_P_VALUES_TEST: GAMMA_INC_P_VALUES stores values of the incomplete Gamma P function. A X F(X) 0.100000 0.030000 0.7382350532339351 0.100000 0.300000 0.9083579897300343 0.100000 1.500000 0.9886559833621947 0.500000 0.075000 0.3014646416966613 0.500000 0.750000 0.7793286380801532 0.500000 3.500000 0.9918490284064972 1.000000 0.100000 0.0951625819640404 1.000000 1.000000 0.6321205588285577 1.000000 5.000000 0.9932620530009145 1.100000 0.100000 0.0720597457605432 1.100000 1.000000 0.5891809618706485 1.100000 5.000000 0.9915368159845525 2.000000 0.150000 0.0101858271111835 2.000000 1.500000 0.4421745996289254 2.000000 7.000000 0.9927049442755639 6.000000 2.500000 0.0420210381953061 6.000000 12.000000 0.9796589705830716 11.000000 16.000000 0.9226039842296428 26.000000 25.000000 0.4470785799755852 41.000000 45.000000 0.7444549220718699 GAMMA_INC_Q_VALUES_TEST: GAMMA_INC_Q_VALUES stores values of the incomplete Gamma Q function. A X F(X) 0.100000 0.030000 0.2617649467660649 0.100000 0.300000 0.0916420102699657 0.100000 1.500000 0.0113440166378053 0.500000 0.075000 0.6985353583033387 0.500000 0.750000 0.2206713619198468 0.500000 3.500000 0.0081509715935027 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.0067379469990855 1.100000 0.100000 0.9279402542394568 1.100000 1.000000 0.4108190381293515 1.100000 5.000000 0.0084631840154475 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.0072950557244361 6.000000 2.500000 0.9579789618046939 6.000000 12.000000 0.0203410294169284 11.000000 16.000000 0.0773960157703571 26.000000 25.000000 0.5529214200244148 41.000000 45.000000 0.2555450779281301 GAMMA_INC_TRICOMI_VALUES_TEST: GAMMA_INC_TRICOMI_VALUES stores values of the Tricomi incomplete Gamma function. A X F(X) 0.100000 0.030000 1.0482926414635041 0.100000 0.300000 1.0245777373695739 0.100000 1.500000 0.9493712443185374 0.500000 0.075000 1.1007932303164920 0.500000 0.750000 0.8998911979655217 0.500000 3.500000 0.5301656062431039 1.000000 0.100000 0.9516258196404043 1.000000 1.000000 0.6321205588285577 1.000000 5.000000 0.1986524106001829 1.100000 0.100000 0.9071784510537487 1.100000 1.000000 0.5891809618706485 1.100000 5.000000 0.1688269752193589 2.000000 0.150000 0.4527034271637121 2.000000 1.500000 0.1965220442795224 2.000000 7.000000 0.0202592845770523 6.000000 2.500000 0.0001721181724480 6.000000 12.000000 0.0000003280858071 11.000000 16.000000 0.0000000000000524 26.000000 25.000000 0.0000000000000000 41.000000 45.000000 0.0000000000000000 GAMMA_LOG_VALUES: GAMMA_LOG_VALUES stores values of the logarithm of the Gamma function. X GAMMA_LOG(X) 0.200000 1.5240638224307841 0.400000 0.7966778177017837 0.600000 0.3982338580692348 0.800000 0.1520596783998375 1.000000 0.0000000000000000 1.100000 -0.0498724412598397 1.200000 -0.0853740900033158 1.300000 -0.1081748095078604 1.400000 -0.1196129141723712 1.500000 -0.1207822376352452 1.600000 -0.1125917656967557 1.700000 -0.0958076974070659 1.800000 -0.0710838729143722 1.900000 -0.0389842759230833 2.000000 0.0000000000000000 3.000000 0.6931471805599453 4.000000 1.7917594692280550 10.000000 12.8018274800814691 20.000000 39.3398841871994946 30.000000 71.2570389671680147 GAMMA_PDF_VALUES_TEST: GAMMA_PDF_VALUES stores values of a Gamma Probability Density Function. Beta Alpha X PDF(X) 1.09209 4.78159 4.94296 0.1672017697220646 2.80848 2.07654 0.209936 0.8522122814089312 1.28789 0.549784 0.0717398 2.122272611165834 3.16983 0.308636 2.58714 6.993771842317114e-05 2.00653 3.77337 4.74318 0.01679379733182281 0.00919186 4.48752 1.97466 6.687464259463117e-10 0.472724 0.0680845 5.1264 0.001295436045931343 4.20424 0.61552 -0.153423 0 1.30151 4.56242 0.504717 0.01189893036865762 1.75814 4.11444 1.45622 0.3658836103539945 GEGENBAUER_POLY_VALUES_TEST: GEGENBAUER_POLY_VALUES returns values of the Gegenbauer polynomials. N A X G(N,A)(X) 0 0.500000 0.200000 1.0000000000000000 1 0.500000 0.200000 0.2000000000000000 2 0.500000 0.200000 -0.4400000000000000 3 0.500000 0.200000 -0.2800000000000000 4 0.500000 0.200000 0.2320000000000000 5 0.500000 0.200000 0.3075200000000000 6 0.500000 0.200000 -0.0805760000000000 7 0.500000 0.200000 -0.2935168000000000 8 0.500000 0.200000 -0.0395648000000000 9 0.500000 0.200000 0.2459712000000000 10 0.500000 0.200000 0.1290720256000000 2 0.000000 0.400000 0.0000000000000000 2 1.000000 0.400000 -0.3600000000000000 2 2.000000 0.400000 -0.0800000000000000 2 3.000000 0.400000 0.8400000000000000 2 4.000000 0.400000 2.3999999999999999 2 5.000000 0.400000 4.5999999999999996 2 6.000000 0.400000 7.4400000000000004 2 7.000000 0.400000 10.9199999999999999 2 8.000000 0.400000 15.0399999999999991 2 9.000000 0.400000 19.8000000000000007 2 10.000000 0.400000 25.1999999999999993 5 3.000000 -0.500000 -9.0000000000000000 5 3.000000 -0.400000 -0.1612800000000000 5 3.000000 -0.300000 -6.6729599999999998 5 3.000000 -0.200000 -8.3750400000000003 5 3.000000 -0.100000 -5.5267200000000001 5 3.000000 0.000000 0.0000000000000000 5 3.000000 0.100000 5.5267200000000001 5 3.000000 0.200000 8.3750400000000003 5 3.000000 0.300000 6.6729599999999998 5 3.000000 0.400000 0.1612800000000000 5 3.000000 0.500000 -9.0000000000000000 5 3.000000 0.600000 -15.4252800000000008 5 3.000000 0.700000 -9.6969600000000007 5 3.000000 0.800000 22.4409600000000005 5 3.000000 0.900000 100.8892799999999994 5 3.000000 1.000000 252.0000000000000000 GEOMETRIC_CDF_VALUES_TEST: GEOMETRIC_CDF_VALUES stores values of the Geometric Probability Cumulative Density Function. X P CDF 1 0.100000 0.1900000000000000 2 0.100000 0.2710000000000000 3 0.100000 0.3439000000000000 10 0.100000 0.6861894039100001 1 0.200000 0.3600000000000000 2 0.200000 0.4880000000000000 3 0.200000 0.5904000000000000 10 0.200000 0.9141006540800000 3 0.300000 0.7599000000000000 3 0.400000 0.8704000000000000 3 0.500000 0.9375000000000000 5 0.500000 0.9843750000000000 10 0.500000 0.9995117187500000 3 0.900000 0.9999000000000000 GOODWIN_VALUES_TEST: GOODWIN_VALUES stores values of the Goodwin function. X FX 0.001953 5.9531540040441655 0.007812 4.5769601268624491 0.031250 3.2288921331902216 0.125000 1.9746110873568719 0.500000 0.9635604620869773 1.000000 0.6051336525033446 1.250000 0.5130550645953220 1.500000 0.4459860282094613 1.875000 0.3734445820687975 2.000000 0.3543359288495306 2.125000 0.3371215651888192 2.500000 0.2943617072936298 3.000000 0.2519349964489722 3.500000 0.2202877822212394 4.000000 0.1957525823769892 4.500000 0.1761630316667070 5.000000 0.1601546947966478 5.750000 0.1409611687619339 6.000000 0.1355498719104907 7.000000 0.1175160506008510 GUD_VALUES_TEST: GUD_VALUES stores values of the Gudermannian function. X FX -2.000000 -1.3017603360460150 -1.000000 -0.8657694832396586 0.000000 0.0000000000000000 0.100000 0.0998337487934866 0.200000 0.1986798470079397 0.500000 0.4803810791337294 1.000000 0.8657694832396586 1.500000 1.1317283452505089 2.000000 1.3017603360460150 2.500000 1.4069935689361539 3.000000 1.4713043411171931 3.500000 1.5104199075457001 4.000000 1.5341691443347329 HERMITE_FUNCTION_VALUES_TEST: HERMITE_FUNCTION_VALUES stores values of the Hermite function. N X Hf(N,X) 0 0.000000 7.5112554446494251e-01 1 0.000000 0.0000000000000000e+00 2 0.000000 -5.3112596601359852e-01 3 0.000000 0.0000000000000000e+00 4 0.000000 4.5996857917732659e-01 5 0.000000 0.0000000000000000e+00 0 1.000000 4.5558067201133251e-01 1 1.000000 6.4428836511347520e-01 2 1.000000 3.2214418255673760e-01 3 1.000000 -2.6302962362333338e-01 4 1.000000 -4.6497507629251100e-01 5 1.000000 -5.8815211851795807e-02 6 1.000000 3.9050525154341059e-01 7 1.000000 2.6318614230640452e-01 8 1.000000 -2.3369114359965229e-01 9 1.000000 -3.5829733614728398e-01 10 1.000000 6.1463444878830410e-02 11 1.000000 3.6783120679848819e-01 12 1.000000 9.1319693091662782e-02 5 0.500000 4.3857509500323211e-01 5 2.000000 -2.6246895279310060e-02 5 3.000000 5.1384261254778185e-01 5 4.000000 9.3555631180617577e-02 HERMITE_POLY_PHYS_VALUES_TEST: HERMITE_POLY_PHYS_VALUES stores values of the physicist's Hermite polynomials. N X H(N,X) 0 5.000000 1.0000000000000000e+00 1 5.000000 1.0000000000000000e+01 2 5.000000 9.8000000000000000e+01 3 5.000000 9.4000000000000000e+02 4 5.000000 8.8120000000000000e+03 5 5.000000 8.0600000000000000e+04 6 5.000000 7.1788000000000000e+05 7 5.000000 6.2116000000000000e+06 8 5.000000 5.2065680000000000e+07 9 5.000000 4.2127120000000000e+08 10 5.000000 3.2755297600000000e+09 11 5.000000 2.4329873600000000e+10 12 5.000000 1.7123708128000000e+11 5 0.000000 0.0000000000000000e+00 5 0.500000 4.1000000000000000e+01 5 1.000000 -8.0000000000000000e+00 5 3.000000 3.8160000000000000e+03 5 10.000000 3.0412000000000000e+06 HERMITE_POLY_PROB_VALUES_TEST: HERMITE_POLY_PROB_VALUES stores values of the probabilist's Hermite polynomials. N X He(N,X) 0 5.000000 1.0000000000000000e+00 1 5.000000 5.0000000000000000e+00 2 5.000000 2.4000000000000000e+01 3 5.000000 1.1000000000000000e+02 4 5.000000 4.7800000000000000e+02 5 5.000000 1.9500000000000000e+03 6 5.000000 7.3600000000000000e+03 7 5.000000 2.5100000000000000e+04 8 5.000000 7.3980000000000000e+04 9 5.000000 1.6910000000000000e+05 10 5.000000 1.7968000000000000e+05 11 5.000000 -7.9260000000000000e+05 12 5.000000 -5.9394800000000000e+06 5 0.000000 0.0000000000000000e+00 5 0.500000 6.2812500000000000e+00 5 1.000000 6.0000000000000000e+00 5 3.000000 1.8000000000000000e+01 5 10.000000 9.0150000000000000e+04 HYPER_1F1_VALUES_TEST: HYPER_1F1_VALUES stores values of the hypergeometric 1F1 function. A B X Hyper_1F1(A,B,C,X) -2.500000 3.300000 0.250000 0.8187992668926519 -0.500000 1.100000 0.250000 0.8828398482803297 0.500000 1.100000 0.250000 1.124502376495263 2.500000 3.300000 0.250000 1.21010493016396 -2.500000 3.300000 1.550000 0.1272304553678157 -0.500000 1.100000 1.550000 0.1232601687154404 0.500000 1.100000 1.550000 2.329795466512829 2.500000 3.300000 1.550000 3.389002026446801 -2.500000 3.300000 2.850000 -0.1881951028251677 -0.500000 1.100000 2.850000 -1.076420380654702 0.500000 1.100000 2.850000 5.752182468090797 2.500000 3.300000 2.850000 9.999856740330408 0.825000 6.700000 0.250000 1.031720896431989 1.100000 6.700000 0.250000 1.042486702924995 1.650000 6.700000 0.250000 1.064311200094909 3.300000 6.700000 0.250000 1.132184436974234 0.825000 6.700000 1.550000 1.232840268856845 1.100000 6.700000 1.550000 1.320065448202734 1.650000 6.700000 1.550000 1.510481152231083 3.300000 6.700000 1.550000 2.230752078594052 0.825000 6.700000 2.850000 1.519728629818314 1.100000 6.700000 2.850000 1.736493817025085 1.650000 6.700000 2.850000 2.249233030766814 3.300000 6.700000 2.850000 4.637773711917896 HYPER_2F1_VALUES_TEST: HYPER_2F1_VALUES stores values of the hypergeometric 2F1 function. A B C X Hyper_2F1(A,B,C,X) -2.500000 3.300000 6.700000 0.250000 0.7235612934899779 -0.500000 1.100000 6.700000 0.250000 0.9791110934527796 0.500000 1.100000 6.700000 0.250000 1.021657814008856 2.500000 3.300000 6.700000 0.250000 1.405156320011213 -2.500000 3.300000 6.700000 0.550000 0.4696143163982161 -0.500000 1.100000 6.700000 0.550000 0.9529619497744632 0.500000 1.100000 6.700000 0.550000 1.051281421394799 2.500000 3.300000 6.700000 0.550000 2.399906290477786 -2.500000 3.300000 6.700000 0.850000 0.2910609592841472 -0.500000 1.100000 6.700000 0.850000 0.9253696791037318 0.500000 1.100000 6.700000 0.850000 1.0865504094807 2.500000 3.300000 6.700000 0.850000 5.738156552618904 3.300000 6.700000 -5.500000 0.250000 15090.66974870461 1.100000 6.700000 -0.500000 0.250000 -104.3117006736435 1.100000 6.700000 0.500000 0.250000 21.17505070776881 3.300000 6.700000 4.500000 0.250000 4.194691581903192 3.300000 6.700000 -5.500000 0.550000 10170777974.04881 1.100000 6.700000 -0.500000 0.550000 -24708.63532248916 1.100000 6.700000 0.500000 0.550000 1372.230454838499 3.300000 6.700000 4.500000 0.550000 58.09272870639465 3.300000 6.700000 -5.500000 0.850000 5.868208761512417e+18 1.100000 6.700000 -0.500000 0.850000 -446350101.47296 1.100000 6.700000 0.500000 0.850000 5383505.756129573 3.300000 6.700000 4.500000 0.850000 20396.91377601966 HYPERGEOMETRIC_CDF_VALUES_TEST: HYPERGEOMETRIC_CDF_VALUES stores values of the Hypergeometric Probability Cumulative Density Function. Sam Suc Pop X FX 10 90 100 7 0.0600185817750058 10 90 100 8 0.2615284665839845 10 90 100 9 0.6695237889132748 10 90 100 10 1.0000000000000000 6 90 100 6 1.0000000000000000 7 90 100 6 0.5332595856827856 8 90 100 6 0.1819495964117640 9 90 100 6 0.0444804701752773 10 10 100 6 0.9999991751316731 10 30 100 6 0.9926860896560750 10 50 100 6 0.8410799901444538 10 70 100 6 0.3459800113391901 10 90 90 0 0.0000000000000000 10 90 200 0 0.0020888881396345 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 HYPERGEOMETRIC_PDF_VALUES_TEST: HYPERGEOMETRIC_PDF_VALUES stores values of the Hypergeometric Probability Density Function. Sam Suc Pop X FX 10 90 100 7 0.0517937053324283 10 90 100 8 0.2015098848089788 10 90 100 9 0.4079953223292903 10 90 100 10 0.3304762110867252 6 90 100 6 0.5223047493549779 7 90 100 6 0.3889503452643453 8 90 100 6 0.1505614239732950 9 90 100 6 0.0392768932104248 10 10 100 6 0.0000309982846552 10 30 100 6 0.0314511609393820 10 50 100 6 0.2114132170316862 10 70 100 6 0.2075776621999210 10 90 90 0 0.0000000000000000 10 90 200 0 0.0020888881396345 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 HYPERGEOMETRIC_U_VALUES_TEST: HYPERGEOMETRIC_U_VALUES stores values of the hypergeometric U function. A B X HyperU(A,B,C,X) -2.500000 3.300000 0.250000 -68.69362872807861 -0.500000 1.100000 0.250000 -0.002971055137476107 0.500000 1.100000 0.250000 1.50086317421778 2.500000 3.300000 0.250000 20.6146882442006 -2.500000 3.300000 1.550000 7.456381546930555 -0.500000 1.100000 1.550000 1.015579376774929 0.500000 1.100000 1.550000 0.7344653893662267 2.500000 3.300000 1.550000 0.280464049418794 -2.500000 3.300000 2.850000 3.450815374144655 -0.500000 1.100000 2.850000 1.515663736875306 0.500000 1.100000 2.850000 0.56042118587935 2.500000 3.300000 2.850000 0.06489714773513422 0.825000 6.700000 0.250000 223432.0235697746 1.100000 6.700000 0.250000 263079.2598074081 1.650000 6.700000 0.250000 269802.9031935128 3.300000 6.700000 0.250000 82809.31133560656 0.825000 6.700000 1.550000 26.46568478313185 1.100000 6.700000 1.550000 28.09350617251606 1.650000 6.700000 1.550000 23.88916462451887 3.300000 6.700000 1.550000 4.533884785707039 0.825000 6.700000 2.850000 3.022446936269484 1.100000 6.700000 2.850000 2.804065091371336 1.650000 6.700000 2.850000 1.926257811148017 3.300000 6.700000 2.850000 0.2302051811586091 I0ML0_VALUES_TEST: I0ML0_VALUES stores values of the I0ML0 function. X FX 0.001953 0.9987575551546175 0.015625 0.9901135823070665 0.125000 0.9241943531002395 0.500000 0.7362426713471427 1.000000 0.5558226918141175 2.000000 0.3421515443446216 4.000000 0.1708717488877471 8.000000 0.0810810087092192 12.000000 0.0534494214410896 16.000000 0.0399503210089232 16.250000 0.0393306374375849 17.000000 0.0375822743428087 20.000000 0.0319124865544804 25.000000 0.0255061468835047 30.000000 0.0212444803178253 40.000000 0.0159254983485517 50.000000 0.0127375069272426 75.000000 0.0084897750814785 100.000000 0.0063668349178454 125.000000 0.0050932843163123 I1ML1_VALUES_TEST: I1ML1_VALUES stores values of the I1ML1 function. X FX 0.001953 0.0009757534615539 0.015625 0.0077609293280609 0.125000 0.0593029664045454 0.500000 0.2039521227673737 1.000000 0.3383947229366764 2.000000 0.4878770672696132 4.000000 0.5901873419657652 8.000000 0.6260453953031215 12.000000 0.6320931527490976 16.000000 0.6341017931323536 16.250000 0.6341796679757813 17.000000 0.6343926863239209 20.000000 0.6350157907325777 25.000000 0.6355961667735945 30.000000 0.6359100182669711 40.000000 0.6362211318175107 50.000000 0.6363648170213361 75.000000 0.6365065349961990 100.000000 0.6365560912630026 125.000000 0.6365790208718393 I4_FACTORIAL_VALUES_TEST: I4_FACTORIAL_VALUES returns values of the factorial function. N N! 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3628800 11 39916800 12 479001600 I4_FACTORIAL2_VALUES_TEST: I4_FACTORIAL2_VALUES returns values of the double factorial function. N N!! 0 1 1 1 2 2 3 3 4 8 5 15 6 48 7 105 8 384 9 945 10 3840 11 10395 12 46080 13 135135 14 645120 15 2027025 I4_FALL_VALUES_TEST: I4_FALL_VALUES returns some exact values of the integer falling factorial function: M N I4_FALL(M,N) 5 0 1 5 1 5 5 2 20 5 3 60 5 4 120 5 5 120 5 6 0 50 0 1 10 1 10 4000 1 4000 10 2 90 18 3 4896 4 4 24 98 3 912576 1 7 0 I4_RISE_VALUES_TEST: I4_RISE_VALUES returns some exact values of the integer rising factorial function: M N I4_RISE(M,N) 5 0 1 5 1 5 5 2 30 5 3 210 5 4 1680 5 5 15120 5 6 151200 50 0 1 INT_VALUES_TEST: INT_VALUES stores values of the integer part of a real number. X INT(X) -2.010000 -2.0000000000000000 -1.990000 -1.0000000000000000 -1.500000 -1.0000000000000000 -1.100000 -1.0000000000000000 -1.010000 -1.0000000000000000 -1.000000 -1.0000000000000000 -0.990000 0.0000000000000000 -0.900000 0.0000000000000000 -0.510000 0.0000000000000000 -0.500000 0.0000000000000000 -0.490000 0.0000000000000000 -0.010000 0.0000000000000000 0.000000 0.0000000000000000 0.010000 0.0000000000000000 0.490000 0.0000000000000000 0.500000 0.0000000000000000 0.510000 0.0000000000000000 0.900000 0.0000000000000000 0.990000 0.0000000000000000 1.000000 1.0000000000000000 1.010000 1.0000000000000000 1.100000 1.0000000000000000 1.500000 1.0000000000000000 1.990000 1.0000000000000000 2.010000 2.0000000000000000 INVERSE_CHI_SQUARE_PDF_VALUES_TEST: INVERSE_CHI_SQUARE_PDF_VALUES returns values of the inverse Chi Square Probability Density Function. DF X PDF 1 0.1 0.08500366602520341 2 0.1 0.3368973499542734 1 0.2 0.3661245640481622 2 0.2 1.026062482798735 1 0.4 0.4518059816704532 2 0.4 0.8953274901880941 3 0.4 1.129514954176133 4 0.4 1.119159362735118 1 1 0.2419707245191433 2 1 0.3032653298563167 3 1 0.2419707245191433 4 1 0.1516326649281584 5 1 0.08065690817304778 3 2 0.0549239111834653 3 3 0.02166329508030457 3 4 0.01100204146138436 3 5 0.006457369034861447 3 6 0.004162370481945731 10 1 0.0007897534631674914 10 2 1.584474249412852e-05 10 3 1.511920090468204e-06 INVERSE_GAMMA_PDF_VALUES_TEST: INVERSE_GAMMA_PDF_VALUES returns values of the inverse gamma Probability Density Function. ALPHA BETA X PDF 1 0.5 1 0.3032653298563167 1 0.5 2 0.09735009788392561 1 0.5 3 0.047026762493923 1 0.5 4 0.02757802820576861 1 2 2 0.1839397205857212 1 3 2 0.1673476201113224 1 4 2 0.1353352832366127 1 5 2 0.1026062482798735 2 2 3 0.07606179541223586 3 2 3 0.02535393180407862 4 2 3 0.005634207067573026 5 2 3 0.0009390345112621711 JACOBI_CN_VALUES_TEST: JACOBI_CN_VALUES returns values of the Jacobi elliptic CN function. A X CN(A,X) 0.000000 0.100000 0.9950041652780258 0.000000 0.200000 0.9800665778412416 0.000000 0.500000 0.8775825618903726 0.000000 1.000000 0.5403023058681397 0.000000 2.000000 -0.4161468365471424 0.500000 0.100000 0.9950124626090582 0.500000 0.200000 0.9801976276784098 0.500000 0.500000 0.8822663948904403 0.500000 1.000000 0.5959765676721407 0.500000 2.000000 -0.1031836155277618 1.000000 0.100000 0.9950207489532265 1.000000 0.200000 0.9803279976447253 1.000000 0.500000 0.8868188839700739 1.000000 1.000000 0.6480542736638853 1.000000 2.000000 0.2658022288340797 1.000000 4.000000 0.0366189934736865 1.000000 -0.200000 0.9803279976447253 1.000000 -0.500000 0.8868188839700739 1.000000 -1.000000 0.6480542736638853 1.000000 -2.000000 0.2658022288340797 JACOBI_DN_VALUES_TEST: JACOBI_DN_VALUES returns values of the Jacobi elliptic DN function. A X DN(A,X) 0.000000 0.100000 1.0000000000000000 0.000000 0.200000 1.0000000000000000 0.000000 0.500000 1.0000000000000000 0.000000 1.000000 1.0000000000000000 0.000000 2.000000 1.0000000000000000 0.500000 0.100000 0.9975093485144243 0.500000 0.200000 0.9901483195224799 0.500000 0.500000 0.9429724257773857 0.500000 1.000000 0.8231610016315963 0.500000 2.000000 0.7108610477840873 1.000000 0.100000 0.9950207489532265 1.000000 0.200000 0.9803279976447253 1.000000 0.500000 0.8868188839700739 1.000000 1.000000 0.6480542736638853 1.000000 2.000000 0.2658022288340797 1.000000 4.000000 0.0366189934736865 1.000000 -0.200000 0.9803279976447253 1.000000 -0.500000 0.8868188839700739 1.000000 -1.000000 0.6480542736638853 1.000000 -2.000000 0.2658022288340797 JACOBI_POLY_VALUES_TEST: JACOBI_POLY_VALUES returns values of the Jacobi polynomial. N A B X J(N,A,B)(X) 0 0.000000 1.000000 0.500000 1.0000000000000000 1 0.000000 1.000000 0.500000 0.2500000000000000 2 0.000000 1.000000 0.500000 -0.3750000000000000 3 0.000000 1.000000 0.500000 -0.4843750000000000 4 0.000000 1.000000 0.500000 -0.1328125000000000 5 0.000000 1.000000 0.500000 0.2753906250000000 5 1.000000 1.000000 0.500000 -0.1640625000000000 5 2.000000 1.000000 0.500000 -1.1748046875000000 5 3.000000 1.000000 0.500000 -2.3613281250000000 5 4.000000 1.000000 0.500000 -2.6162109375000000 5 5.000000 1.000000 0.500000 0.1171875000000000 5 0.000000 2.000000 0.500000 0.4218750000000000 5 0.000000 3.000000 0.500000 0.5048828125000000 5 0.000000 4.000000 0.500000 0.5097656250000000 5 0.000000 5.000000 0.500000 0.4306640625000000 5 0.000000 1.000000 -1.000000 -6.0000000000000000 5 0.000000 1.000000 -0.800000 0.0386200000000000 5 0.000000 1.000000 -0.600000 0.8118400000000000 5 0.000000 1.000000 -0.400000 0.0366600000000000 5 0.000000 1.000000 -0.200000 -0.4851200000000000 5 0.000000 1.000000 0.000000 -0.3125000000000000 5 0.000000 1.000000 0.200000 0.1891200000000000 5 0.000000 1.000000 0.400000 0.4023400000000000 5 0.000000 1.000000 0.600000 0.0121600000000000 5 0.000000 1.000000 0.800000 -0.4396200000000000 5 0.000000 1.000000 1.000000 1.0000000000000000 JACOBI_SN_VALUES_TEST: JACOBI_SN_VALUES returns values of the Jacobi elliptic SN function. A X SN(A,X) 0.000000 0.100000 0.0998334166468282 0.000000 0.200000 0.1986693307950612 0.000000 0.500000 0.4794255386042030 0.000000 1.000000 0.8414709848078965 0.000000 2.000000 0.9092974268256817 0.500000 0.100000 0.0997506854746248 0.500000 0.200000 0.1980217429819704 0.500000 0.500000 0.4707504736556573 0.500000 1.000000 0.8030018248956439 0.500000 2.000000 0.9946623253580177 1.000000 0.100000 0.0996679946249558 1.000000 0.200000 0.1973753202249040 1.000000 0.500000 0.4621171572600098 1.000000 1.000000 0.7615941559557649 1.000000 2.000000 0.9640275800758169 1.000000 4.000000 0.9993292997390670 1.000000 -0.200000 -0.1973753202249040 1.000000 -0.500000 -0.4621171572600098 1.000000 -1.000000 -0.7615941559557649 1.000000 -2.000000 -0.9640275800758169 JED_CE_VALUES_TEST: JED_CE_VALUES returns: JED, a Julian Ephemeris Date, and YMDF, the corresponding year, month, day, fraction. JED Y M D F 0.000000 -4713 1 1 0.500000 1.000000 -4713 1 2 0.500000 259261.000000 -4004 10 26 0.500000 347998.500000 -3761 10 8 0.000000 584282.500000 -3114 9 6 0.000000 588465.750000 -3102 2 18 0.250000 758325.500000 -2637 3 8 0.000000 1438178.500000 -776 7 9 0.000000 1446389.500000 -753 1 1 0.000000 1448637.500000 -747 2 26 0.000000 1448637.500000 -747 2 26 0.000000 1607708.500000 -312 9 1 0.000000 1607738.500000 -312 10 1 0.000000 1713262.500000 -23 8 29 0.000000 1721422.500000 -1 12 31 0.000000 1721423.500000 1 1 1 0.000000 1721425.500000 1 1 3 0.000000 1721425.500000 1 1 3 0.000000 1724220.500000 8 8 29 0.000000 1741959.500000 57 3 24 0.000000 1749994.500000 79 3 24 0.000000 1825029.500000 284 8 29 0.000000 1862836.500000 388 3 3 0.000000 1922867.500000 552 7 11 0.000000 1936747.500000 590 7 12 0.000000 1940351.500000 600 5 24 0.000000 1948320.500000 622 3 19 0.000000 1948438.500000 622 7 15 0.000000 1948439.500000 622 7 16 0.000000 1952062.500000 632 6 16 0.000000 1952067.500000 632 6 21 0.000000 2114872.500000 1078 3 17 0.000000 2289425.500000 1556 2 9 0.000000 2299160.000000 1582 10 4 0.500000 2299161.000000 1582 10 15 0.500000 2333269.500000 1676 3 4 0.000000 2361221.000000 1752 9 13 0.500000 2361222.000000 1752 9 14 0.500000 2372547.500000 1783 9 18 0.000000 2375839.500000 1792 9 22 0.000000 2394646.500000 1844 3 21 0.000000 2394710.500000 1844 5 24 0.000000 2400000.500000 1858 11 17 0.000000 2415020.310000 1899 12 31 0.810000 2440587.500000 1970 1 1 0.000000 2444244.500000 1980 1 6 0.000000 2450138.500000 1996 2 25 0.000000 2451544.500000 2000 1 1 0.000000 2453073.830000 2004 3 9 0.330000 2456284.500000 2012 12 23 0.000000 2913943.000000 3266 1 1 0.500000 JED_MJD_VALUES_TEST: JED_MJD_VALUES returns: JED, a Julian Ephemeris Date, and MJD, the corresponding Modified Julian Day count. JED MJD 1507231.500000 -892769.000000 1660037.500000 -739963.000000 1746893.500000 -653107.000000 1770641.500000 -629359.000000 1892731.500000 -507269.000000 1931579.500000 -468421.000000 1974851.500000 -425149.000000 2091164.500000 -308836.000000 2121509.500000 -278491.000000 2155779.500000 -244221.000000 2174029.500000 -225971.000000 2191584.500000 -208416.000000 2195261.500000 -204739.000000 2229274.500000 -170726.000000 2245580.500000 -154420.000000 2266100.500000 -133900.000000 2288542.500000 -111458.000000 2290901.500000 -109099.000000 2323140.500000 -76860.000000 2334848.500000 -65152.000000 2348020.500000 -51980.000000 2366978.500000 -33022.000000 2385648.500000 -14352.000000 2392825.500000 -7175.000000 2416223.500000 16223.000000 2425848.500000 25848.000000 2430266.500000 30266.000000 2430833.500000 30833.000000 2431004.500000 31004.000000 2448698.500000 48698.000000 2450138.500000 50138.000000 2465737.500000 65737.000000 2486076.500000 86076.000000 JED_RD_VALUES: JED_RD_VALUES returns: JED, a Julian Ephemeris Date, and RD, the corresponding Reingold Dershowitz Day count. JED RD 1507231.500000 -214193.000000 1660037.500000 -61387.000000 1746893.500000 25469.000000 1770641.500000 49217.000000 1892731.500000 171307.000000 1931579.500000 210155.000000 1974851.500000 253427.000000 2091164.500000 369740.000000 2121509.500000 400085.000000 2155779.500000 434355.000000 2174029.500000 452605.000000 2191584.500000 470160.000000 2195261.500000 473837.000000 2229274.500000 507850.000000 2245580.500000 524156.000000 2266100.500000 544676.000000 2288542.500000 567118.000000 2290901.500000 569477.000000 2323140.500000 601716.000000 2334848.500000 613424.000000 2348020.500000 626596.000000 2366978.500000 645554.000000 2385648.500000 664224.000000 2392825.500000 671401.000000 2416223.500000 694799.000000 2425848.500000 704424.000000 2430266.500000 708842.000000 2430833.500000 709409.000000 2431004.500000 709580.000000 2448698.500000 727274.000000 2450138.500000 728714.000000 2465737.500000 744313.000000 2486076.500000 764652.000000 JED_WEEKDAY_VALUES_TEST: JED_WEEKDAY_VALUES returns Julian Ephemeris Dates (JED) and the corresponding weekday JED # Weekday 1507231.500000 1 Sunday 1660037.500000 4 Wednesday 1746893.500000 4 Wednesday 1770641.500000 1 Sunday 1892731.500000 4 Wednesday 1931579.500000 2 Monday 1974851.500000 7 Saturday 2091164.500000 1 Sunday 2121509.500000 1 Sunday 2155779.500000 6 Friday 2174029.500000 7 Saturday 2191584.500000 6 Friday 2195261.500000 1 Sunday 2229274.500000 1 Sunday 2245580.500000 4 Wednesday 2266100.500000 7 Saturday 2288542.500000 7 Saturday 2290901.500000 7 Saturday 2323140.500000 4 Wednesday 2334848.500000 1 Sunday 2348020.500000 6 Friday 2366978.500000 1 Sunday 2385648.500000 2 Monday 2392825.500000 4 Wednesday 2416223.500000 1 Sunday 2425848.500000 1 Sunday 2430266.500000 2 Monday 2430833.500000 2 Monday 2431004.500000 5 Thursday 2448698.500000 3 Tuesday 2450138.500000 1 Sunday 2465737.500000 4 Wednesday 2486076.500000 1 Sunday KEI0_VALUES_TEST: KEI0_VALUES stores values of the Kelvin function KEI of order 0. X FX 0.000000 0.0000000000000000 0.500000 -0.6715816950943676 1.000000 -0.4949946365187199 1.500000 -0.3313955623385585 2.000000 -0.2024000677647043 2.500000 -0.1106960991556749 3.000000 -0.0511218840459868 3.500000 -0.0160025685182712 4.000000 0.0021983992949725 4.500000 0.0097209185401520 5.000000 0.0111875865098696 KEI1_VALUES_TEST: KEI1_VALUES stores values of the Kelvin function KEI of order 1. X FX 0.500000 -1.0511820854125229 1.000000 -0.2419959664297382 1.500000 0.0010086809850099 2.000000 0.0800493978070667 2.500000 0.0933137881353575 3.000000 0.0802702225239222 3.500000 0.0593762564762269 4.000000 0.0391660107691713 4.500000 0.0230021602469025 5.000000 0.0115777543932525 KER0_VALUES_TEST: KER0_VALUES stores values of the Kelvin function KER of order 0. X FX 0.500000 0.8559058721186342 1.000000 0.2867062087283160 1.500000 0.0529349154877104 2.000000 -0.0416645139915095 2.500000 -0.0696879725890453 3.000000 -0.0670292333037987 3.500000 -0.0526392772422412 4.000000 -0.0361788478995476 4.500000 -0.0219998750466738 5.000000 -0.0115117271994907 KER1_VALUES_TEST: KER1_VALUES stores values of the Kelvin function KER of order 1. X FX 0.500000 -1.5224034065320899 1.000000 -0.7403222768419827 1.500000 -0.4170442851662574 2.000000 -0.2308059295181230 2.500000 -0.1172561358598705 3.000000 -0.0498983077875149 3.500000 -0.0127232493618166 4.000000 0.0053512964602774 4.500000 0.0120909041351587 5.000000 0.0127373904842186 LAGUERRE_ASSOCIATED_VALUES_TEST: LAGUERRE_ASSOCIATED_VALUES stores values of the associated Laguerre function. N M X L(N,M)(X) 1 0 0.000000 1.0000000000000000 2 0 0.000000 1.0000000000000000 3 0 0.000000 1.0000000000000000 4 0 0.000000 1.0000000000000000 5 0 0.000000 1.0000000000000000 1 1 0.500000 1.5000000000000000 2 1 0.500000 1.6250000000000000 3 1 0.500000 1.4791666666666670 4 1 0.500000 1.1484375000000000 3 0 0.200000 0.4586666666666667 3 1 0.200000 2.8786666666666672 3 2 0.200000 8.0986666666666665 3 3 0.200000 17.1186666666666696 4 2 0.250000 10.4532877604166696 5 2 0.250000 13.2901936848958293 6 3 0.250000 56.2245364718966982 7 3 0.250000 74.8472934177943614 8 4 0.250000 323.8912982762806223 9 4 0.250000 442.6100000097533211 10 5 0.250000 1936.8765722882499176 LAGUERRE_GENERAL_VALUES_TEST: LAGUERRE_GENERAL_VALUES stores values of the generalized Laguerre function. N A X L(N,A)(X) 5 0.000000 0.250000 0.0372639973958333 5 0.250000 0.250000 0.3494791666666667 5 0.500000 0.250000 0.8710042317708333 5 0.750000 0.250000 1.6723958333333331 5 1.500000 0.250000 6.6576253255208329 5 2.500000 0.250000 23.9572672526041686 5 5.000000 0.250000 203.1344319661457973 8 1.200000 0.000000 12.8419399680000001 8 1.200000 0.200000 5.3599248015873018 8 1.200000 0.400000 0.9204589064126985 8 1.200000 0.600000 -1.3415851148571429 8 1.200000 0.800000 -2.1197263075555561 8 1.200000 1.000000 -1.9591936583492060 0 5.200000 0.750000 1.0000000000000000 1 5.200000 0.750000 5.4500000000000002 2 5.200000 0.750000 17.2012500000000017 3 5.200000 0.750000 41.1039375000000007 4 5.200000 0.750000 82.3974585937500024 5 5.200000 0.750000 146.0179186171874903 6 5.200000 0.750000 235.9204608298828134 LAGUERRE_POLYNOMIAL_VALUES_TEST: LAGUERRE_POLYNOMIAL_VALUES stores values of the Laguerre polynomials. N X L(N)(X) 0 1.000000 1.0000000000000000 1 1.000000 0.0000000000000000 2 1.000000 -0.5000000000000000 3 1.000000 -0.6666666666666667 4 1.000000 -0.6250000000000000 5 1.000000 -0.4666666666666667 6 1.000000 -0.2569444444444444 7 1.000000 -0.0404761904761905 8 1.000000 0.1539930555555556 9 1.000000 0.3097442680776014 10 1.000000 0.4189459325396825 11 1.000000 0.4801341790925124 12 1.000000 0.4962122235082305 5 0.500000 -0.4455729166666667 5 3.000000 0.8500000000000000 5 5.000000 -3.1666666666666670 5 10.000000 34.3333333333333286 LAMBERT_W_VALUES_TEST: LAMBERT_W_VALUES stores values of the Lambert W function. X W(X) 0.000000 0.0000000000000000 0.500000 0.3517337112491958 1.000000 0.5671432904097840 1.500000 0.7258613577662263 2.000000 0.8526055020137255 2.500000 0.9585863567287028 2.718282 1.0000000000000000 3.000000 1.0499088949640401 3.500000 1.1302893269741361 4.000000 1.2021678731970431 4.500000 1.2672378143074350 5.000000 1.3267246652422000 5.500000 1.3815453794450410 6.000000 1.4324047758983001 6.500000 1.4798568301738511 7.000000 1.5243452049841439 7.500000 1.5662309537823880 8.000000 1.6058119963201780 10.000000 1.7455280027406990 100.000000 3.3856301402900502 1000.000000 5.2496028524015959 1000000.000000 11.3833580861400492 TEST100: LAPLACE_CDF_VALUES stores values of the Laplace Cumulative Density Function. Mu Beta X CDF(X) 0.000000 1.000000 0.000000 0.5000000000000000 0.000000 1.000000 1.000000 0.8160602794142788 0.000000 1.000000 2.000000 0.9323323583816937 0.000000 1.000000 3.000000 0.9751064658160680 0.000000 2.000000 1.000000 0.6967346701436833 0.000000 3.000000 1.000000 0.6417343447131054 0.000000 4.000000 1.000000 0.6105996084642976 0.000000 5.000000 1.000000 0.5906346234610091 1.000000 2.000000 1.000000 0.5000000000000000 2.000000 2.000000 1.000000 0.3032653298563167 3.000000 2.000000 1.000000 0.1839397205857212 4.000000 2.000000 1.000000 0.1115650800742149 LEGENDRE_ASSOCIATED_VALUES_TEST: LEGENDRE_ASSOCIATED_VALUES stores values of the associated Legendre polynomials. N M X P(N,M)(X) 1 0 0.000000 0.0000000000000000 2 0 0.000000 -0.5000000000000000 3 0 0.000000 0.0000000000000000 4 0 0.000000 0.3750000000000000 5 0 0.000000 0.0000000000000000 1 1 0.500000 -0.8660254037844386 2 1 0.500000 -1.2990381056766580 3 1 0.500000 -0.3247595264191645 4 1 0.500000 1.3531646934131849 3 0 0.200000 -0.2800000000000000 3 1 0.200000 1.1757550765359250 3 2 0.200000 2.8799999999999999 3 3 0.200000 -14.1090609184311102 4 2 0.250000 -3.9550781250000000 5 2 0.250000 -9.9975585937500000 6 3 0.250000 82.6531144410048455 7 3 0.250000 20.2444283681515209 8 4 0.250000 -423.7997531890869141 9 4 0.250000 1638.3206248283390778 10 5 0.250000 -20256.8738922722513962 LEGENDRE_ASSOCIATED_NORMALIZED_VALUES_TEST: LEGENDRE_ASSOCIATED_NORMALIZED_VALUES stores values of the normalized associated Legendre polynomials. N M X P(N,M)(X) 0 0 0.500000 0.7071067811865475 1 0 0.500000 0.6123724356957945 1 1 0.500000 -0.7500000000000000 2 0 0.500000 -0.1976423537605237 2 1 0.500000 -0.8385254915624211 2 2 0.500000 0.7261843774138907 3 0 0.500000 -0.8184875533567997 3 1 0.500000 -0.1753901900050285 3 2 0.500000 0.9606516343087123 3 3 0.500000 -0.6792832849776299 4 0 0.500000 -0.6131941618102092 4 1 0.500000 0.6418623720763665 4 2 0.500000 0.4716705890038619 4 3 0.500000 -1.0189249274664449 4 4 0.500000 0.6239615396237876 5 0 0.500000 0.2107022704608181 5 1 0.500000 0.8256314721961969 5 2 0.500000 -0.3982651281554632 5 3 0.500000 -0.7040399320721435 5 4 0.500000 1.0347231552722891 5 5 0.500000 -0.5667412129155530 LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES_TEST: LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES stores values of the associated Legendre polynomials, normalized for a sphere. N M X P(N,M)(X) 0 0 0.500000 0.2820947917738781 1 0 0.500000 0.2443012559514600 1 1 0.500000 -0.2992067103010745 2 0 0.500000 -0.0788478913131300 2 1 0.500000 -0.3345232717786446 2 2 0.500000 0.2897056515173922 3 0 0.500000 -0.3265292910163510 3 1 0.500000 -0.0699705623606466 3 2 0.500000 0.3832445536624809 3 3 0.500000 -0.2709948227475519 4 0 0.500000 -0.2446290772414100 4 1 0.500000 0.2560660384200185 4 2 0.500000 0.1881693403754876 4 3 0.500000 -0.4064922341213279 4 4 0.500000 0.2489246395003027 5 0 0.500000 0.0840580442633982 5 1 0.500000 0.3293793022891428 5 2 0.500000 -0.1588847984307093 5 3 0.500000 -0.2808712959945307 5 4 0.500000 0.4127948151484925 5 5 0.500000 -0.2260970318780046 LEGENDRE_FUNCTION_Q_VALUES_TEST: LEGENDRE_FUNCTION_Q_VALUES stores values of the Legendre Q functions. N X Q(N)(X) 0 0.250000 0.2554128118829953 1 0.250000 -0.9361467970292512 2 0.250000 -0.4787614548274669 3 0.250000 0.4246139251747229 4 0.250000 0.5448396833845414 5 0.250000 -0.0945132826167347 6 0.250000 -0.4973516573531213 7 0.250000 -0.1499018843853194 8 0.250000 0.3649161918783626 9 0.250000 0.3055676545072885 10 0.250000 -0.1832799367995643 3 0.000000 0.6666666666666667 3 0.100000 0.6268672028763330 3 0.200000 0.5099015515315237 3 0.300000 0.3232754180589764 3 0.400000 0.0802611373814819 3 0.500000 -0.1986547714794823 3 0.600000 -0.4828663183349136 3 0.700000 -0.7252886849144387 3 0.800000 -0.8454443502398846 3 0.900000 -0.6627096245052618 LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES_TEST: LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES stores values of the normalized Legendre polynomials. N X Pn(N)(X) 0 0.25 0.7071067811865475 1 0.25 0.3061862178478972 2 0.25 -0.642337649721702 3 0.25 -0.6284815141846855 4 0.25 0.3345637065282053 5 0.25 0.7967179601799685 6 0.25 0.06189376866246124 7 0.25 -0.766588850921089 8 0.25 -0.4444760242953344 9 0.25 0.5450094674858101 10 0.25 0.7167706229835538 3 0 0 3 0.1 -0.2759472322745781 3 0.2 -0.5238320341483518 3 0.3 -0.7155919752205163 3 0.4 -0.823164625090267 3 0.5 -0.8184875533567997 3 0.6 -0.6734983296193094 3 0.7 -0.360134523476992 3 0.8 0.1496662954709581 3 0.9 0.8839665576253438 3 1 1.870828693386971 LEGENDRE_POLYNOMIAL_VALUES_TEST: LEGENDRE_POLYNOMIAL_VALUES stores values of the Legendre polynomials. N X P(N)(X) 0 0.25 1 1 0.25 0.25 2 0.25 -0.40625 3 0.25 -0.3359375 4 0.25 0.15771484375 5 0.25 0.3397216796875 6 0.25 0.0242767333984375 7 0.25 -0.2799186706542969 8 0.25 -0.1524540185928345 9 0.25 0.1768244206905365 10 0.25 0.2212002165615559 3 0 0 3 0.1 -0.1475 3 0.2 -0.28 3 0.3 -0.3825 3 0.4 -0.44 3 0.5 -0.4375 3 0.6 -0.36 3 0.7 -0.1925 3 0.8 0.08 3 0.9 0.4725 3 1 1 LEGENDRE_SHIFTED_POLYNOMIAL_VALUES_TEST: LEGENDRE_SHIFTED_POLYNOMIAL_VALUES stores values of the shifted Legendre polynomials. N X P(N)(X) 0 0.625 1 1 0.625 0.25 2 0.625 -0.40625 3 0.625 -0.3359375 4 0.625 0.15771484375 5 0.625 0.3397216796875 6 0.625 0.0242767333984375 7 0.625 -0.2799186706542969 8 0.625 -0.1524540185928345 9 0.625 0.1768244206905365 10 0.625 0.2212002165615559 3 0.5 0 3 0.55 -0.1475 3 0.6 -0.28 3 0.65 -0.3825 3 0.7 -0.44 3 0.75 -0.4375 3 0.8 -0.36 3 0.85 -0.1925 3 0.9 0.08 3 0.95 0.4725 3 1 1 LERCH_VALUES_TEST: LERCH_VALUES stores values of the Lerch function. Z S A FX 1.000000 2 0.000000 1.6449340668482260 1.000000 3 0.000000 1.2020569031595940 1.000000 10 0.000000 1.0009945751278180 0.500000 2 1.000000 1.1644810529300249 0.500000 3 1.000000 1.0744263872160800 0.500000 10 1.000000 1.0004926412120141 0.333333 2 2.000000 0.2959190697935714 0.333333 3 2.000000 0.1394507503935608 0.333333 10 2.000000 0.0009823175058446 0.100000 2 3.000000 0.1177910993911311 0.100000 3 3.000000 0.0386844792229896 0.100000 10 3.000000 0.0000170314961419 LOBACHEVSKY_VALUES_TEST: LOBACHEVSKY_VALUES stores values of the Lobachevsky function. X FX 0.001953 0.0000000012417639 0.007812 0.0000000794733448 0.031250 0.0000050867598186 0.125000 0.0003260309790121 0.500000 0.0213805368154082 1.000000 0.1875381690208383 1.500000 0.8305119997188365 2.000000 1.8854362426679034 2.500000 2.1315988986516410 3.000000 2.1771120185613428 4.000000 2.2921027921896653 5.000000 3.9137195028784495 6.000000 4.3513563983836425 7.000000 4.4200644968478189 10.000000 6.5656013133623832 15.000000 10.8255046615045991 20.000000 13.3655128554742273 30.000000 21.1310026856399595 50.000000 34.8382365894491173 100.000000 69.6570624378373964 LOBATTO_POLYNOMIAL_VALUES_TEST: LOBATTO_POLYNOMIAL_VALUES stores values of the completed Lobatto polynomials. N X Lo(N)(X) 1 0.250000 0.9375000000000000 2 0.250000 0.7031250000000000 3 0.250000 -0.9667968750000000 4 0.250000 -1.5014648437500000 5 0.250000 0.3639221191406250 6 0.250000 2.0019149780273442 7 0.250000 0.6597948074340820 8 0.250000 -1.9344413280487061 9 0.250000 -1.7699411138892169 10 0.250000 1.2152436655014749 3 -1.000000 0.0000000000000000 3 -0.900000 0.8692500000000000 3 -0.800000 1.1879999999999999 3 -0.700000 1.1092500000000001 3 -0.600000 0.7680000000000000 3 -0.500000 0.2812500000000000 3 -0.400000 -0.2520000000000000 3 -0.300000 -0.7507500000000000 3 -0.200000 -1.1519999999999999 3 -0.100000 -1.4107499999999999 3 0.000000 -1.5000000000000000 3 0.100000 -1.4107499999999999 3 0.200000 -1.1519999999999999 3 0.300000 -0.7507500000000000 3 0.400000 -0.2520000000000000 3 0.500000 0.2812500000000000 3 0.600000 0.7680000000000000 3 0.700000 1.1092500000000001 3 0.800000 1.1879999999999999 3 0.900000 0.8692500000000000 3 1.000000 0.0000000000000000 LOBATTO_POLYNOMIAL_DERIVATIVES_TEST: LOBATTO_POLYNOMIAL_DERIVATIVES stores derivatives of the completed Lobatto polynomials. N X Lo'(N)(X) 1 0.250000 -0.5000000000000000 2 0.250000 2.4375000000000000 3 0.250000 4.0312500000000000 4 0.250000 -3.1542968750000000 5 0.250000 -10.1916503906250000 6 0.250000 -1.0196228027343750 7 0.250000 15.6754455566406303 8 0.250000 10.9766893386840803 9 0.250000 -15.9141978621482796 10 0.250000 -24.3320238217711413 3 -1.000000 12.0000000000000000 3 -0.900000 5.6699999999999999 3 -0.800000 0.9600000000000000 3 -0.700000 -2.3100000000000001 3 -0.600000 -4.3200000000000003 3 -0.500000 -5.2500000000000000 3 -0.400000 -5.2800000000000002 3 -0.300000 -4.5899999999999999 3 -0.200000 -3.3599999999999999 3 -0.100000 -1.7700000000000000 3 0.000000 0.0000000000000000 3 0.100000 1.7700000000000000 3 0.200000 3.3599999999999999 3 0.300000 4.5899999999999999 3 0.400000 5.2800000000000002 3 0.500000 5.2500000000000000 3 0.600000 4.3200000000000003 3 0.700000 2.3100000000000001 3 0.800000 -0.9600000000000000 3 0.900000 -5.6699999999999999 3 1.000000 -12.0000000000000000 LOG_VALUES_TEST: LOG_VALUES stores values of the natural logarithm function. X FX 0.000010 -11.5129254649702286 0.010000 -4.6051701859880918 0.100000 -2.3025850929940459 0.200000 -1.6094379124341003 0.300000 -1.2039728043259359 0.400000 -0.9162907318741551 0.500000 -0.6931471805599453 0.600000 -0.5108256237659907 0.700000 -0.3566749439387324 0.800000 -0.2231435513142098 0.900000 -0.1053605156578263 1.000000 0.0000000000000000 2.000000 0.6931471805599453 3.000000 1.0986122886681098 3.141593 1.1447298858494002 5.000000 1.6094379124341003 10.000000 2.3025850929940459 20.000000 2.9957322735539909 100.000000 4.6051701859880918 123456789.000000 18.6314017661680182 LOG_NORMAL_CDF_VALUES: LOG_NORMAL_CDF_VALUES stores values of the Log Normal Cumulative Density Function. Mu Sigma X CDF(X) 1.000000 0.500000 1.000000 0.0227501319481792 1.000000 0.500000 2.000000 0.2697049307349095 1.000000 0.500000 3.000000 0.5781741008028732 1.000000 0.500000 4.000000 0.7801170895122241 1.000000 2.000000 2.000000 0.4390310097476894 1.000000 3.000000 2.000000 0.4592655190218048 1.000000 4.000000 2.000000 0.4694258497695908 1.000000 5.000000 2.000000 0.4755320473858733 2.000000 2.000000 3.000000 0.3261051056816658 3.000000 2.000000 3.000000 0.1708799040927608 4.000000 2.000000 3.000000 0.0734325635795206 5.000000 2.000000 3.000000 0.0255467373616176 LOG_SERIES_CDF_VALUES_TEST: LOG_SERIES_CDF_VALUES stores values of the Log Series Cumulative Density Function. T N CDF(X) 0.100000 1 0.9491221581029903 0.111111 1 0.9433541128559735 0.125000 1 0.9361094611773272 0.142857 1 0.9267370278044118 0.166667 1 0.9141358246245129 0.200000 1 0.8962840235449100 0.250000 1 0.8690148741955517 0.333333 1 0.8221011541254772 0.500000 1 0.7213475204444817 0.666667 1 0.6068261510845583 0.750000 1 0.5410106403333613 0.800000 1 0.4970679476476894 0.833333 1 0.4650921887927060 0.857149 1 0.4404842934597863 0.875000 1 0.4207860535926143 0.888889 1 0.4045507673897055 0.900000 1 0.3908650337129266 0.990000 1 0.2149757685421097 0.990000 0 0.0000000000000000 0.990000 1 0.2149757685421097 0.990000 2 0.3213887739704539 0.990000 3 0.3916213575531612 0.990000 4 0.4437690508633213 0.990000 5 0.4850700239649681 0.990000 6 0.5191433267738267 0.990000 7 0.5480569580144867 0.990000 8 0.5731033910767085 0.990000 9 0.5951442521714636 0.990000 10 0.6147826594068904 LOG10_VALUES_TEST: LOG10_VALUES stores values of the base 10 logarithm function. X FX 0.000010 -5.0000000000000000 0.010000 -2.0000000000000000 0.100000 -1.0000000000000000 0.200000 -0.6989700043360189 0.300000 -0.5228787452803375 0.400000 -0.3979400086720376 0.500000 -0.3010299956639812 0.600000 -0.2218487496163564 0.700000 -0.1549019599857432 0.800000 -0.0969100130080564 0.900000 -0.0457574905606751 1.000000 0.0000000000000000 2.000000 0.3010299956639812 3.000000 0.4771212547196624 3.141593 0.4971498726941339 5.000000 0.6989700043360189 10.000000 1.0000000000000000 20.000000 1.3010299956639813 100.000000 2.0000000000000000 123456789.000000 8.0915149771692700 LOGARITHMIC_INTEGRAL_VALUES_TEST: LOGARITHMIC_INTEGAL_VALUES stores values of the logarithmic integral function. X LI(X) 0.000000 0.0000000000000000 0.100000 -0.0323897895932910 0.200000 -0.0851264867287941 0.300000 -0.1574149028946895 0.400000 -0.2529494192126213 0.500000 -0.3786710430610880 0.600000 -0.5468514142104171 0.700000 -0.7809468775455607 0.800000 -1.1340119573823271 0.900000 -1.7758006834235249 0.950000 -2.4436225538732250 0.975000 -3.1241900505072109 1.031250 -2.8729355103291199 1.062500 -2.1642825241382071 1.125000 -1.4403512962794081 1.250000 -0.6864884538258716 1.500000 0.1250649863152964 2.000000 1.0451637801174929 4.000000 2.9675850950390510 8.000000 5.2537182995589307 16.000000 8.5197164637110596 32.000000 13.6050921770917199 64.000000 21.9346683280510000 128.000000 36.0425483172294392 256.000000 60.5130653379173324 512.000000 103.7211171690372993 1024.000000 181.0780396816944915 2048.000000 321.1144156746836984 LOGISTIC_CDF_VALUES_TEST: LOGISTIC_CDF_VALUES stores values of the Logistic Cumulative Density Function. Mu Beta X CDF(X) 1.000000 0.500000 1.000000 0.5000000000000000 1.000000 0.500000 2.000000 0.8807970779778824 1.000000 0.500000 3.000000 0.9820137900379085 1.000000 0.500000 4.000000 0.9975273768433652 1.000000 2.000000 2.000000 0.6224593312018546 1.000000 3.000000 2.000000 0.5825702064623147 1.000000 4.000000 2.000000 0.5621765008857981 1.000000 5.000000 2.000000 0.5498339973124780 2.000000 2.000000 3.000000 0.6224593312018546 3.000000 2.000000 3.000000 0.5000000000000000 4.000000 2.000000 3.000000 0.3775406687981454 5.000000 2.000000 3.000000 0.2689414213699951 MERTENS_VALUES: MERTENS_VALUES returns values of the Mertens function. N MERTENS(N) 1 1 2 0 3 -1 4 -1 5 -2 6 -1 7 -2 8 -2 9 -2 10 -1 11 -2 12 -2 100 1 1000 2 10000 -23 MITTAG_LEFFLER_EA_VALUES_TEST: MITTAG_LEFFLER_EA_VALUES stores values of the Mittag-Leffler one parameter function E(A;X). A X E(A;X) 0.250000 0.000000 1.0000000000000000 0.250000 -2.500000 0.2525646348870172 0.250000 -5.000000 0.1427989464258737 0.250000 -7.500000 0.0994231091392936 0.250000 -10.000000 0.0762370352397216 1.750000 0.000000 1.0000000000000000 1.750000 -12.500000 -0.2579027070618285 1.750000 -25.000000 0.2716853059670252 1.750000 -37.500000 0.0184657991660401 1.750000 -50.000000 -0.1397073896421940 2.250000 0.000000 1.0000000000000000 2.250000 -25.000000 -1.0221218438234969 2.250000 -50.000000 1.8608445225896111 2.250000 -75.000000 2.6446154459968909 2.250000 -100.000000 0.7762512036620307 1.000000 -5.000000 0.0067379469990457 2.000000 -5.000000 -0.6172728764571668 3.000000 -5.000000 0.2010457248089053 4.000000 -5.000000 0.7922864454196143 5.000000 -5.000000 0.9583402225672250 6.000000 -5.000000 0.9930556077474290 7.000000 -5.000000 0.9990079367947130 8.000000 -5.000000 0.9998759920646870 9.000000 -5.000000 0.9999862213403840 10.000000 -5.000000 0.9999986221340380 MITTAG_LEFFLER_EAB_VALUES_TEST: MITTAG_LEFFLER_EAB_VALUES stores values of the Mittag-Leffler two parameter function E(A,B;X). A B X E(A,B;X) 1.000000 -0.250000 0.000000 -0.1947001957678512 1.000000 -0.250000 2.500000 0.6821152851737027 1.000000 -0.250000 5.000000 0.0396671329463129 1.500000 -1.250000 0.000000 -0.7783327874361643 1.500000 -1.250000 5.000000 0.0376189576668972 1.500000 -1.250000 10.000000 0.0000026538646597 3.000000 -2.750000 1.000000 0.5521129475536116 3.000000 -2.750000 1.100000 0.6561318862220054 3.000000 -2.750000 1.200000 0.7417555514147703 1.500000 -5.000000 5.000000 0.0283627999653323 1.500000 -5.000000 10.000000 0.0000023827660801 1.500000 -5.000000 15.000000 0.0000000000105734 1.500000 5.000000 5.000000 0.0652406907307750 2.000000 5.000000 5.000000 0.0492669388452307 2.500000 5.000000 5.000000 0.0444084851633765 2.000000 2.000000 1.000000 2.1781835566085701 2.000000 2.000000 2.000000 1.3682988720085909 2.000000 2.000000 3.000000 0.5890917783042855 MOEBIUS_VALUES_TEST: MOEBIUS_VALUES returns values of the Moebius function. N MU(N) 1 1 2 -1 3 -1 4 0 5 -1 6 1 7 -1 8 0 9 0 10 1 11 -1 12 0 13 -1 14 1 15 1 16 0 17 -1 18 0 19 -1 20 0 MULTINOMIAL_PDF_VALUES_TEST: MULTINOMIAL_PDF_VALUES stores values of the Multinomial PDF. Given M possible outcomes on a single trial, with each outcome having probability P, PDF is the probability that after N trials, outcome I occurred X(I) times. N M I P X PDF() 1 0.7000 2 2 0.3000 1 3 2 0.441 1 0.7000 2 2 0.3000 2 4 2 0.2646 1 0.5000 2 2 0.5000 1 3 2 0.375 1 0.6000 1 2 0.0000 1 3 0.4000 1 3 3 0 1 0.6000 3 2 0.1000 0 3 0.1000 0 4 0.1000 0 5 0.1000 0 3 5 0.216 1 0.6000 2 2 0.1000 1 3 0.1000 0 4 0.1000 0 5 0.1000 0 3 5 0.108 1 0.6000 1 2 0.1000 0 3 0.1000 2 4 0.1000 0 5 0.1000 0 3 5 0.018 1 0.6000 1 2 0.1000 0 3 0.1000 0 4 0.1000 1 5 0.1000 1 3 5 0.036 1 0.6000 0 2 0.1000 0 3 0.1000 0 4 0.1000 3 5 0.1000 0 3 5 0.001 1 0.6000 0 2 0.1000 1 3 0.1000 1 4 0.1000 1 5 0.1000 0 3 5 0.006 NEGATIVE_BINOMIAL_CDF_VALUES_TEST: NEGATIVE_BINOMIAL_CDF_VALUES stores values of the Negative Binomial Cumulative Density Function. F S P NBN_CDF(X) 4 4 0.500000 0.6367187500000000 3 5 0.500000 0.3632812500000000 2 6 0.500000 0.1445312500000000 3 4 0.500000 0.5000000000000000 2 5 0.500000 0.2265625000000000 1 6 0.500000 0.0625000000000000 2 4 0.500000 0.3437500000000000 1 5 0.500000 0.1093750000000000 0 6 0.500000 0.0156250000000000 2 4 0.400000 0.1792000000000000 1 5 0.400000 0.0409600000000000 0 6 0.400000 0.0040960000000000 2 4 0.300000 0.0704700000000000 1 5 0.300000 0.0109350000000000 0 6 0.300000 0.0007290000000000 11 1 0.300000 0.9861587127990000 10 2 0.300000 0.9149749500510000 9 3 0.300000 0.7471846521450000 17 1 0.100000 0.8499053647030009 16 2 0.100000 0.5497160941090026 15 3 0.100000 0.2662040052146710 9 1 0.100000 0.6513215599000000 8 2 0.100000 0.2639010709000000 7 3 0.100000 0.0701908264000000 2 0 0.010000 1.0000000000000000 1 1 0.010000 0.0199000000000000 0 2 0.010000 0.0001000000000000 NINE_J_VALUES_TEST: NINE_J_VALUES returns values of the Wigner 9J coefficient. J1 J2 J3 J4 J5 J6 J7 J8 J9 NINE_J 1.00 8.00 7.00 6.50 7.50 7.50 6.00 10.00 6.00 0.0004270039294528 1.50 8.00 7.00 6.50 7.50 7.50 6.00 10.00 6.00 -0.0012289154510585 2.00 8.00 7.00 6.50 7.50 7.50 6.00 10.00 6.00 -0.0001944260688401 1.00 3.00 2.00 4.00 1.50 3.00 3.50 2.00 2.00 0.0033384199238856 1.50 3.00 2.00 4.00 1.50 3.00 3.50 2.00 2.00 -0.0007958936865080 2.00 3.00 2.00 4.00 1.50 3.00 3.50 2.00 2.00 -0.0043382086902520 0.50 0.50 1.00 2.00 1.00 1.50 1.50 0.50 1.50 0.0537914353639919 1.00 0.50 1.00 2.00 1.00 1.50 1.50 0.50 1.50 0.0062112999374994 1.50 0.50 1.00 2.00 1.00 1.50 1.50 0.50 1.50 0.0304290309725092 NORMAL_01_CDF_VALUES_TEST: NORMAL_01_CDF_VALUES stores values of the Normal 01 Cumulative Density Function. X CDF(X) 0.0000000000000000 0.5000000000000000 0.1000000000000000 0.5398278372770290 0.2000000000000000 0.5792597094391030 0.3000000000000000 0.6179114221889526 0.4000000000000000 0.6554217416103242 0.5000000000000000 0.6914624612740131 0.6000000000000000 0.7257468822499270 0.7000000000000000 0.7580363477769270 0.8000000000000000 0.7881446014166033 0.9000000000000000 0.8159398746532405 1.0000000000000000 0.8413447460685429 1.5000000000000000 0.9331927987311419 2.0000000000000000 0.9772498680518208 2.5000000000000000 0.9937903346742240 3.0000000000000000 0.9986501019683699 3.5000000000000000 0.9997673709209645 4.0000000000000000 0.9999683287581669 NORMAL_01_PDF_VALUES_TEST: NORMAL_01_PDF_VALUES stores values of the Normal 01 Probability Density Function. X PDF(X) -2.252653624140994 0.03155059887555709 3.650540612071437 0.0005094586261557538 2.636073871461605 0.01235886992552887 0.4935635421351536 0.353192862601275 -0.6775433481923101 0.3171212685764107 -3.471050120671749 0.0009653372813755943 -1.939377660943641 0.06083856556197816 -3.120345651740235 0.003066504313116445 -3.649368017767143 0.0005116437388114821 1.0717256984193 0.2246444116615346 NORMAL_CDF_VALUES_TEST: NORMAL_CDF_VALUES stores values of the Normal Cumulative Density Function. Mu Sigma X CDF(X) 1.000000 0.500000 1.000000 0.5000000000000000 1.000000 0.500000 2.000000 0.9772498680518208 1.000000 0.500000 3.000000 0.9999683287581669 1.000000 0.500000 4.000000 0.9999999990134124 1.000000 2.000000 2.000000 0.6914624612740131 1.000000 3.000000 2.000000 0.6305586598182364 1.000000 4.000000 2.000000 0.5987063256829237 1.000000 5.000000 2.000000 0.5792597094391030 2.000000 2.000000 3.000000 0.6914624612740131 3.000000 2.000000 3.000000 0.5000000000000000 4.000000 2.000000 3.000000 0.3085375387259869 5.000000 2.000000 3.000000 0.1586552539314571 NORMAL_PDF_VALUES_TEST: NORMAL_PDF_VALUES stores values of the Normal Probability Density Function. Mu Sigma X PDF(X) -56.316341 4.785956 -46.854240 0.0118077593721326 12.339089 2.135005 6.781057 0.0063078491744789 -48.484442 0.638788 -50.232822 0.0147514774470322 26.793142 0.402463 26.671290 0.9468437743011001 -19.738744 3.797900 -12.964347 0.0214031229994179 -99.632326 4.497770 -103.660016 0.0593995996735349 -81.091050 0.166723 -80.731832 0.2348929157422787 68.169490 0.703209 66.091559 0.0072075156785713 -47.939400 4.571170 -58.535445 0.0059443968976567 -29.674268 4.132148 -35.447731 0.0363766316577132 OMEGA_VALUES_TEST: OMEGA_VALUES returns values of the Omega function. N OMEGA(N) 1 0 2 1 3 1 4 1 5 1 6 2 7 1 8 1 9 1 10 2 30 3 101 1 210 4 1320 4 1764 3 2003 1 2310 5 2827 2 8717 2 12553 1 30030 6 510510 7 9699690 8 OWEN_VALUES_TEST: OWEN_VALUES stores values of the Owen T function. H A T 0.062500 0.250000 0.0389119302347014 6.500000 0.437500 0.0000000000200058 7.000000 0.968750 0.0000000000006399 4.781250 0.062500 0.0000001063297480 2.000000 0.500000 0.0086250779855215 1.000000 0.999997 0.0667418089782286 1.000000 0.500000 0.0430646911207854 1.000000 1.000000 0.0667418821657010 1.000000 2.000000 0.0784681869930841 1.000000 3.000000 0.0792995047488726 0.500000 0.500000 0.0644886028475038 0.500000 1.000000 0.1066710629614485 0.500000 2.000000 0.1415806036539784 0.500000 3.000000 0.1510840430760184 0.250000 0.500000 0.0713466338227178 0.250000 1.000000 0.1201285306350883 0.250000 2.000000 0.1666128410939293 0.250000 3.000000 0.1847501847929859 0.125000 0.500000 0.0731727332750039 0.125000 1.000000 0.1237630544953746 0.125000 2.000000 0.1737438887583106 0.125000 3.000000 0.1951190307092811 0.007812 0.500000 0.0737893803536555 0.007812 1.000000 0.1249951430754052 0.007812 2.000000 0.1761984774738108 0.007812 3.000000 0.1987772386442824 0.007812 10.000000 0.2340886964802671 0.007812 100.000000 0.2479460829231492 PARTITION_COUNT_VALUES_TEST: PARTITION_COUNT_VALUES returns values of the integer partition count function. N P(N) 0 1 1 1 2 2 3 3 4 5 5 7 6 11 7 15 8 22 9 30 10 42 11 56 12 77 13 101 14 135 15 176 16 231 17 297 18 385 19 490 20 627 PARTITION_DISTINCT_COUNT_VALUES_TEST: PARTITION_DISTINCT_COUNT_VALUES returns values of the integer distinct partition count function. N Q(N) 0 1 1 1 2 1 3 2 4 2 5 3 6 4 7 5 8 6 9 8 10 10 11 12 12 15 13 18 14 22 15 27 16 32 17 38 18 46 19 54 20 64 PHI_VALUES_TEST: PHI_VALUES returns values of the PHI function. N PHI(N) 1 1 2 1 3 2 4 2 5 4 6 2 7 6 8 4 9 6 10 4 20 8 30 8 40 16 50 20 60 16 100 40 149 148 500 200 750 200 999 648 PI_VALUES_TEST: PI_VALUES returns values of the PI function. N PI(N) 10 4 20 8 30 10 40 12 50 15 60 17 70 19 80 22 90 24 100 25 1000 168 10000 1229 100000 9592 1000000 78498 10000000 664579 100000000 5761455 1000000000 50847534 POISSON_CDF_VALUES_TEST: POISSON_CDF_VALUES returns values of the Poisson Cumulative Density Function. A X POISSON_CDF(A,X) 0.020000 0 0.9801986733067553 0.100000 0 0.9048374180359596 0.100000 1 0.9953211598395555 0.500000 0 0.6065306597126334 0.500000 1 0.9097959895689501 0.500000 2 0.9856123220330293 1.000000 0 0.3678794411714423 1.000000 1 0.7357588823428846 1.000000 2 0.9196986029286058 1.000000 3 0.9810118431238462 2.000000 0 0.1353352832366127 2.000000 1 0.4060058497098381 2.000000 2 0.6766764161830635 2.000000 3 0.8571234604985470 5.000000 0 0.0067379469990855 5.000000 1 0.0404276819945128 5.000000 2 0.1246520194830811 5.000000 3 0.2650259152973617 5.000000 4 0.4404932850652124 5.000000 5 0.6159606548330631 5.000000 6 0.7621834629729387 POLYLOGARITHM_VALUES_TEST: POLYLOGARITHM_VALUES stores values of the polylogarithm. N Z FX 2 1.000000 1.6449340668482260 3 1.000000 1.2020569031595940 10 1.000000 1.0009945751278180 2 0.500000 0.5822405264650125 3 0.500000 0.5372131936080402 10 0.500000 0.5002463206060068 2 0.333333 0.3662132299770635 3 0.333333 0.3488278611548401 10 0.333333 0.3334424797228716 2 0.100000 0.1026177910993911 3 0.100000 0.1012886844792230 10 0.100000 0.1000097826564961 POLYOMINO_CHIRAL_COUNT_VALUES_TEST: POLYOMINO_CHIRAL_COUNT_VALUES returns counts of the number of chiral polyominoes. Order Number 0 1 1 1 2 1 3 2 4 7 5 18 6 60 7 196 8 704 9 2500 10 9189 11 33896 12 126759 13 476270 14 1802312 15 6849777 16 26152418 17 100203194 18 385221143 19 1485200848 20 5741256764 21 22245940545 22 86383382827 23 336093325058 24 1309998125640 25 5114451441106 26 19998172734786 27 78306011677182 28 307022182222506 29 1205243866707468 30 4736694001644862 POLYOMINO_FIXED_COUNT_VALUES_TEST: POLYOMINO_FIXED_COUNT_VALUES returns counts of the number of fixed polyominoes. Order Number 0 1 1 1 2 2 3 6 4 19 5 63 6 216 7 760 8 2725 9 9910 10 36446 11 135268 12 505861 13 1903890 14 7204874 15 27394666 16 104592937 17 400795844 18 1540820542 19 5940738676 20 22964779660 21 88983512783 22 345532572678 23 1344372335524 24 5239988770268 25 20457802016011 26 79992676367108 27 313224032098244 28 1228088671826973 POLYOMINO_FREE_COUNT_VALUES_TEST: POLYOMINO_FREE_COUNT_VALUES returns counts of the number of free polyominoes. Order Number 0 1 1 1 2 1 3 2 4 5 5 12 6 35 7 108 8 369 9 1285 10 4655 11 17073 12 63600 13 238591 14 901971 15 3426576 16 13079255 17 50107909 18 192622052 19 742624232 20 2870671950 21 11123060678 22 43191857688 23 168047007728 24 654999700403 25 2557227044764 26 9999088822075 27 39153010938487 28 153511100594603 PRANDTL_VALUES_TEST: PRANDTL_VALUES stores values of the Prandtl number of water as a function of temperature and pressure. T P Pr(T,P) 0.000000 1.000000 13.5000000000000000 0.000000 5.000000 13.4800000000000004 0.000000 10.000000 13.4600000000000009 0.000000 25.000000 13.3900000000000006 0.000000 50.000000 13.2699999999999996 0.000000 75.000000 13.1500000000000004 0.000000 100.000000 13.0399999999999991 0.000000 125.000000 12.9299999999999997 0.000000 150.000000 12.8300000000000001 0.000000 175.000000 12.7300000000000004 0.000000 200.000000 12.6300000000000008 0.000000 225.000000 12.5299999999999994 0.000000 250.000000 12.4299999999999997 0.000000 275.000000 12.3399999999999999 0.000000 300.000000 12.2500000000000000 0.000000 350.000000 12.0800000000000001 0.000000 400.000000 11.9199999999999999 0.000000 450.000000 11.7699999999999996 0.000000 500.000000 11.6199999999999992 0.000000 550.000000 11.4800000000000004 0.000000 600.000000 11.3599999999999994 0.000000 650.000000 11.2300000000000004 0.000000 700.000000 11.1199999999999992 0.000000 800.000000 10.9100000000000001 0.000000 900.000000 10.7200000000000006 0.000000 1000.000000 10.5500000000000007 25.000000 1.000000 6.1369999999999996 50.000000 1.000000 3.5550000000000002 75.000000 1.000000 2.3780000000000001 100.000000 1.000000 1.0000000000000000 150.000000 1.000000 0.9740000000000000 200.000000 1.000000 0.9600000000000000 400.000000 1.000000 0.9240000000000000 600.000000 1.000000 0.8990000000000000 800.000000 1.000000 0.8820000000000000 PRIME_VALUES_TEST: PRIME_VALUES returns values of the prime function. N P[N] 1 2 2 3 4 7 8 19 16 53 32 131 64 311 128 719 256 1619 512 3671 1000 7919 2000 17389 4000 37813 8000 81799 16000 176081 32000 376127 64000 800573 128000 1698077 256000 3588941 512000 7559173 1024000 15881419 2048000 33283031 4096000 69600977 8192000 145253029 PSAT_VALUES_TEST: PSAT_VALUES stores values of the saturation pressure of water as a function of temperature. T PSAT(T) 0.010000 0.0061173000000000 1.000000 0.0065716000000000 5.000000 0.0087260000000000 50.000000 0.1234400000000000 100.000000 1.0132000000000001 125.000000 2.3201000000000001 150.000000 4.7572000000000001 200.000000 15.5370000000000008 250.000000 39.7370000000000019 300.000000 85.8379999999999939 350.000000 165.2100000000000080 373.976000 220.5500000000000114 PSI_VALUES_TEST: PSI_VALUES stores values of the PSI function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 R8_FACTORIAL_VALUES_TEST: R8_FACTORIAL_VALUES stores values of the factorial function (using real arithmetic). N Factorial(N) 0 1.0000000000000000e+00 1 1.0000000000000000e+00 2 2.0000000000000000e+00 3 6.0000000000000000e+00 4 2.4000000000000000e+01 5 1.2000000000000000e+02 6 7.2000000000000000e+02 7 5.0400000000000000e+03 8 4.0320000000000000e+04 9 3.6288000000000000e+05 10 3.6288000000000000e+06 11 3.9916800000000000e+07 12 4.7900160000000000e+08 13 6.2270208000000000e+09 14 8.7178291200000000e+10 15 1.3076743680000000e+12 16 2.0922789888000000e+13 17 3.5568742809600000e+14 18 6.4023737057280000e+15 19 1.2164510040883200e+17 20 2.4329020081766400e+18 25 1.5511210043330990e+25 50 3.0414093201713381e+64 100 9.3326215443944151e+157 150 5.7133839564458547e+262 R8_FACTORIAL_LOG_VALUES_TEST: R8_FACTORIAL_LOG_VALUES stores values of the logarithm of the factorial function (using real arithmetic). N Log(Factorial(N)) 0 0.0000000000000000 1 0.0000000000000000 2 0.6931471805599453 3 1.7917594692280550 4 3.1780538303479462 5 4.7874917427820458 6 6.5792512120101012 7 8.5251613610654147 8 10.6046029027452509 9 12.8018274800814709 10 15.1044125730755194 11 17.5023078458738901 12 19.9872144956618882 13 22.5521638531234210 14 25.1912211827386798 15 27.8992713838408903 16 30.6718601060806684 17 33.5050734501368908 18 36.3954452080330526 19 39.3398841871994875 20 42.3356164607534922 25 58.0036052229805179 50 148.4777669517729919 100 363.7393755555635266 150 605.0201058494236577 500 2611.3304584601560236 1000 5912.1281784881630301 R8_FACTORIAL2_VALUES_TEST: R8_FACTORIAL2_VALUES returns values of the double factorial function. N N!! 0 1 1 1 2 2 3 3 4 8 5 15 6 48 7 105 8 384 9 945 10 3840 11 10395 12 46080 13 135135 14 645120 15 2.02702e+06 R8_FALL_VALUES_TEST: R8_FALL_VALUES returns some exact values of the falling factorial function: X N R8_FALL(X,N) 5.000000 4 120 5.250000 4 163.16 5.500000 4 216.562 5.750000 4 281.66 6.000000 4 360 7.500000 0 1 7.500000 1 7.5 7.500000 2 48.75 7.500000 3 268.125 7.500000 4 1206.56 7.500000 5 4222.97 7.500000 6 10557.4 7.500000 7 15836.1 7.500000 8 7918.07 7.500000 9 -3959.03 R8_RISE_VALUES_TEST: R8_RISE_VALUES returns some exact values of the rising factorial function: X N R8_RISE(X,N) 5.000000 4 1680 5.250000 4 1962.6 5.500000 4 2279.06 5.750000 4 2631.97 6.000000 4 3024 7.500000 0 1 7.500000 1 7.5 7.500000 2 63.75 7.500000 3 605.625 7.500000 4 6359.06 7.500000 5 73129.2 7.500000 6 914115 7.500000 7 1.23406e+07 7.500000 8 1.78938e+08 7.500000 9 2.77354e+09 RAYLEIGH_CDF_VALUES_TEST: RAYLEIGH_CDF_VALUES stores values of the Rayleigh CDF. SIGMA X FX 0.500000 1.000000 0.8646647167633873 0.500000 2.000000 0.9996645373720975 0.500000 3.000000 0.9999999847700203 0.500000 4.000000 0.9999999999999870 1.000000 2.000000 0.8646647167633873 2.000000 2.000000 0.3934693402873666 3.000000 2.000000 0.1992625970831920 4.000000 2.000000 0.1175030974154046 5.000000 2.000000 0.0768836536133642 SCALED_INVERSE_CHI_SQUARE_PDF_VALUES_TEST: SCALED_INVERSE_CHI_SQUARE_PDF_VALUES returns values of the scaled inverse Chi Square Probability Density Function. DF XI X PDF 1 0.5 0.1 0.7322491280963244 2 0.5 0.1 0.3368973499542734 1 0.5 0.2 0.9036119633409063 2 0.5 0.2 1.026062482798735 1 0.5 0.4 0.5968580144169457 2 0.5 0.4 0.8953274901880941 1 1 0.1 0.08500366602520341 2 1 0.1 0.004539992976248485 1 1 0.2 0.3661245640481622 2 1 0.2 0.1684486749771367 1 1 0.4 0.4518059816704532 2 1 0.4 0.5130312413993675 1 2 0.1 0.0008099910956089117 2 2 0.1 4.122307244877116e-07 1 2 0.2 0.04250183301260171 2 2 0.2 0.002269996488124243 1 2 0.4 0.1830622820240811 2 2 0.4 0.08422433748856833 SECVIR_VALUES_TEST: SECVIR_VALUES stores values of the second virial coefficient of water as a function of temperature. T VIR(T) 0.000000 -98.9599999999999937 5.000000 -90.0799999999999983 10.000000 -82.2900000000000063 20.000000 -69.3599999999999994 30.000000 -59.1899999999999977 40.000000 -51.0700000000000003 60.000000 -39.1300000000000026 90.000000 -27.8099999999999987 120.000000 -20.8299999999999983 150.000000 -16.2100000000000009 180.000000 -12.9800000000000004 210.000000 -10.6300000000000008 240.000000 -8.8499999999999996 300.000000 -6.3899999999999997 400.000000 -4.0300000000000002 500.000000 -2.7100000000000000 700.000000 -1.3200000000000001 1000.000000 -0.3900000000000000 2000.000000 0.5300000000000000 SHI_VALUES_TEST: SHI_VALUES stores values of the hyperbolic sine integral function. X SHI(X) 0.500000 0.5069967498196672 0.600000 0.6121303965633808 0.700000 0.7193380189288998 0.800000 0.8289965633789345 0.900000 0.9414978265114335 1.000000 1.0572508753757290 1.200000 1.3002503610220570 1.400000 1.5617133883610019 1.600000 1.8458141413585041 1.800000 2.1572903434259012 2.000000 2.5015674333549760 2.500000 3.5493404062244349 3.000000 4.9734404758598068 3.500000 6.9661620675049418 4.000000 9.8173269112330335 4.500000 13.9678850493471494 SI_VALUES_TEST: SI_VALUES stores values of the sine integral function. X SI(X) 0.500000 0.4931074180430667 0.600000 0.5881288096080801 0.700000 0.6812222391166113 0.800000 0.7720957854819966 0.900000 0.8604707107452929 1.000000 0.9460830703671830 1.200000 1.1080471990137191 1.400000 1.2562267327792180 1.600000 1.3891804858704380 1.800000 1.5058167802555791 2.000000 1.6054129768026950 2.500000 1.7785201734438270 3.000000 1.8486525279994681 3.500000 1.8331253986659970 4.000000 1.7582031389490529 4.500000 1.6541404143792440 SIGMA_VALUES_TEST: SIGMA_VALUES returns values of the SIGMA function. N SIGMA(N) 1 1 2 3 3 4 4 7 5 6 6 12 7 8 8 15 9 13 10 18 30 72 127 128 128 255 129 176 210 576 360 1170 617 618 815 984 816 2232 1000 2340 SIN_VALUES_TEST: SIN_VALUES stores values of the sine function. X FX 0.000000 0.0000000000000000 0.261799 0.2588190451025207 0.500000 0.4794255386042030 0.523599 0.5000000000000000 0.785398 0.7071067811865476 1.000000 0.8414709848078965 1.047198 0.8660254037844386 1.570796 1.0000000000000000 2.000000 0.9092974268256817 3.000000 0.1411200080598672 3.141593 0.0000000000000000 4.000000 -0.7568024953079282 5.000000 -0.9589242746631385 SIN_DEGREE_VALUES_TEST: SIN_DEGREE_VALUES stores values of the sine function. X FX -5.000000 -0.0871557427476582 0.000000 0.0000000000000000 1.000000 0.0174524064372835 2.000000 0.0348994967025010 3.000000 0.0523359562429438 4.000000 0.0697564737441253 5.000000 0.0871557427476582 10.000000 0.1736481776669304 15.000000 0.2588190451025207 30.000000 0.5000000000000000 45.000000 0.7071067811865476 60.000000 0.8660254037844386 75.000000 0.9659258262890683 85.000000 0.9961946980917455 86.000000 0.9975640502598242 87.000000 0.9986295347545738 88.000000 0.9993908270190958 89.000000 0.9998476951563913 90.000000 1.0000000000000000 91.000000 0.9998476951563913 105.000000 0.9659258262890683 180.000000 0.0000000000000000 SIN_POWER_INT_VALUES_TEST: SIN_POWER_INT_VALUES returns values of the N-th power of the SIN function. A B N FX 10.000000 20.000000 0 10.0000000000000000 0.000000 1.000000 1 0.4596976941318603 0.000000 1.000000 2 0.2726756432935796 0.000000 1.000000 3 0.1789405625488581 0.000000 1.000000 4 0.1240255653152068 0.000000 1.000000 5 0.0889743964515759 0.000000 2.000000 5 0.9039312384814995 1.000000 2.000000 5 0.8149568420299235 0.000000 1.000000 10 0.0218875224217298 0.000000 1.000000 11 0.0170234393740693 SINH_VALUES_TEST: SINH_VALUES stores values of the hyperbolic sine function. X FX -5.000000 -74.2032105777887523 -1.000000 -1.1752011936438014 0.000000 0.0000000000000000 0.100000 0.1001667500198440 0.200000 0.2013360025410940 0.300000 0.3045202934471426 0.400000 0.4107523258028155 0.500000 0.5210953054937474 0.600000 0.6366535821482413 0.700000 0.7585837018395335 0.800000 0.8881059821876230 0.900000 1.0265167257081753 1.000000 1.1752011936438014 2.000000 3.6268604078470186 3.000000 10.0178749274099026 4.000000 27.2899171971277532 5.000000 74.2032105777887523 10.000000 11013.2328747033934633 SIX_J_VALUES_TEST: SIX_J_VALUES returns values of the Wigner 6J coefficient. J1 J2 J3 J4 J5 J6 SIX_J 1.00 8.00 7.00 6.50 7.50 7.50 0.0349090513837330 2.00 8.00 7.00 6.50 7.50 7.50 -0.0374302503965979 3.00 8.00 7.00 6.50 7.50 7.50 0.0189086639095956 4.00 8.00 7.00 6.50 7.50 7.50 0.0073424482549286 5.00 8.00 7.00 6.50 7.50 7.50 -0.0235893518508179 6.00 8.00 7.00 6.50 7.50 7.50 0.0191347695521544 7.00 8.00 7.00 6.50 7.50 7.50 0.0012880173977242 8.00 8.00 7.00 6.50 7.50 7.50 -0.0193001836629053 9.00 8.00 7.00 6.50 7.50 7.50 0.0167730594938289 10.00 8.00 7.00 6.50 7.50 7.50 0.0055011472748509 11.00 8.00 7.00 6.50 7.50 7.50 -0.0213543979089683 12.00 8.00 7.00 6.50 7.50 7.50 0.0034603644514354 13.00 8.00 7.00 6.50 7.50 7.50 0.0252095005479559 14.00 8.00 7.00 6.50 7.50 7.50 0.0148399056122171 15.00 8.00 7.00 6.50 7.50 7.50 0.0027085776806332 SOUND_VALUES_TEST: SOUND_VALUES stores values of the speed of sound in water as a function of temperature and pressure. T P C(T,P) 0.000000 1.000000 1401.0000000000000000 100.000000 1.000000 472.8000000000000114 200.000000 1.000000 533.7000000000000455 300.000000 1.000000 585.7000000000000455 350.000000 1.000000 609.5000000000000000 400.000000 1.000000 632.2000000000000455 500.000000 1.000000 674.6000000000000227 600.000000 1.000000 713.8999999999999773 850.000000 1.000000 802.0000000000000000 1100.000000 1.000000 880.1000000000000227 1600.000000 1.000000 1017.7999999999999545 2000.000000 1.000000 1115.9000000000000909 0.000000 5.000000 1401.7000000000000455 0.000000 10.000000 1402.5999999999999091 0.000000 50.000000 1409.5999999999999091 0.000000 100.000000 1418.0999999999999091 0.000000 250.000000 1443.0999999999999091 0.000000 500.000000 1484.5999999999999091 0.000000 1000.000000 1577.0999999999999091 0.000000 2500.000000 1913.4000000000000909 SPHERE_UNIT_AREA_VALUES_TEST: SPHERE_UNIT_AREA_VALUES stores values of the area of the unit sphere in various dimensions. N Area 1 2.0000000000000000 2 6.2831853071795862 3 12.5663706143591707 4 19.7392088021787195 5 26.3189450695716189 6 31.0062766802998198 7 33.0733617923198082 8 32.4696970113341479 9 29.6865801246483585 10 25.5016403987734499 11 20.7251426732889001 12 16.0231532262550687 13 11.8381738121826796 14 8.3897034104910890 15 5.7216492123495666 16 3.7652900857422908 17 2.3966788175913640 18 1.4786259590003079 19 0.8858104195716824 20 0.5161378278002812 SPHERE_UNIT_VOLUME_VALUES_TEST: SPHERE_UNIT_VOLUME_VALUES stores values of the volume of the unit sphere in various dimensions. N Volume 1 2.0000000000000000 2 3.1415926535897931 3 4.1887902047863914 4 4.9348022005446790 5 5.2637890139143249 6 5.1677127800499703 7 4.7247659703314007 8 4.0587121264167676 9 3.2985089027387069 10 2.5501640398773451 11 1.8841038793899001 12 1.3352627688545891 13 0.9106287547832831 14 0.5992645293207921 15 0.3814432808233045 16 0.2353306303588932 17 0.1409811069171390 18 0.0821458866111282 19 0.0466216010300885 20 0.0258068913900141 SPHERICAL_HARMONIC_VALUES_TEST: SPHERICAL_HARMONIC_VALUES stores values of the spherical harmonic function. L M THETA PHI YR YI 0 0 0.523599 1.047198 0.2820947917738781 0.0000000000000000 1 0 0.523599 1.047198 0.4231421876608172 0.0000000000000000 2 1 0.523599 1.047198 -0.1672616358893223 -0.2897056515173922 3 2 0.523599 1.047198 -0.1106331731112457 0.1916222768312404 4 3 0.523599 1.047198 0.1354974113737760 0.0000000000000000 5 5 0.261799 0.628319 0.0005390423109044 0.0000000000000000 5 4 0.261799 0.628319 -0.0051466904429519 0.0037392894852833 5 3 0.261799 0.628319 0.0137100436134949 -0.0421951755232080 5 2 0.261799 0.628319 0.0609635202226554 0.1876264225575173 5 1 0.261799 0.628319 -0.4170400640977983 -0.3029973424491321 4 2 0.628319 0.785398 0.0000000000000000 0.4139385503112256 4 2 1.884956 0.785398 0.0000000000000000 -0.1003229830187463 4 2 3.141593 0.785398 0.0000000000000000 0.0000000000000000 4 2 4.398230 0.785398 0.0000000000000000 -0.1003229830187463 4 2 5.654867 0.785398 0.0000000000000000 0.4139385503112256 3 -1 0.392699 0.448799 0.3641205966137958 -0.1753512375142586 3 -1 0.392699 0.897598 0.2519792711195075 -0.3159720118970196 3 -1 0.392699 1.346397 0.0899303606570430 -0.3940106541811563 3 -1 0.392699 1.795196 -0.0899303606570430 -0.3940106541811563 3 -1 0.392699 2.243995 -0.2519792711195075 -0.3159720118970196 SQRT_VALUES_TEST: SQRT_VALUES returns some values of the SQRT function. X SQRT(X) 0.000000 0.0000000000000000 0.000000 0.0000900000004095 0.090000 0.3000000000000000 0.100000 0.3162277660168379 0.400000 0.6324555320336759 1.000000 1.0000000000000000 2.000000 1.4142135623730949 3.000000 1.7320508075688770 3.141593 1.7724538509055161 19.000000 4.3588989435406740 29.000000 5.3851648071345037 71.000000 8.4261497731763590 97.000000 9.8488578017961057 123456789.000000 11111.1110605555604707 STIRLING1_VALUES_TEST: STIRLING1_VALUES returns values of the Stirling numbers of the first kind. N M S1 1 2 0 2 2 1 3 2 -3 4 2 11 5 2 -50 6 2 274 7 2 -1764 8 2 13068 9 2 -109584 10 2 1026576 8 3 -13132 8 4 6769 8 5 -1960 8 6 322 8 7 -28 8 8 1 STIRLING2_VALUES_TEST: STIRLING2_VALUES returns values of the Stirling numbers of the second kind. N M S2 1 2 0 2 2 1 3 2 3 4 2 7 5 2 15 6 2 31 7 2 63 8 2 127 9 2 255 10 2 511 8 3 966 8 4 1701 8 5 1050 8 6 266 8 7 28 8 8 1 STROMGEN_VALUES_TEST: STROMGEN_VALUES stores values of the Stromgen function. X FX 0.001953 0.0000000000000002 0.007812 0.0000000000002248 0.031250 0.0000000002324502 0.125000 0.0000002471956148 0.500000 0.0002899261098983 1.000000 0.0106981463908097 1.500000 0.0897076509644247 2.000000 0.4004960571959289 3.000000 3.0504104398079095 4.000000 11.3677048584394260 4.125000 12.9606794053247878 4.500000 18.5487139447485063 5.000000 27.8662738219031212 6.000000 51.9633340716993217 8.000000 108.6101674789122882 10.000000 153.7890331655662237 15.000000 193.0266553255872282 20.000000 196.3685016600654194 30.000000 196.5194676600821424 50.000000 196.5195692086831514 STRUVE_H0_VALUES_TEST: STRUVE_H0_VALUES stores values of the Struve H0 function. X H0(X) 0.001953 0.0012433974658847 -0.007812 -0.0049735582423748 0.062500 0.0397714690545369 -0.250000 -0.1580524600165331 1.000000 0.5686566270482879 1.250000 0.6659839931489991 2.000000 0.7908588495080959 -4.000000 -0.1350145734224864 7.500000 0.2008647966816450 11.000000 -0.1114209780026199 11.500000 -0.1702680486598989 -16.000000 -0.1354493180818647 20.000000 0.0943936980813234 25.000000 -0.1018248201600151 -30.000000 0.0960984215541621 50.000000 -0.0853376748261190 75.000000 -0.0768822906370527 -80.000000 0.0476638335914183 100.000000 -0.0708787516896473 -125.000000 0.0657529080733528 STRUVE_H1_VALUES_TEST: STRUVE_H1_VALUES stores values of the Struve H1 function. X H1(X) 0.001953 0.0000008095036958 -0.007812 0.0000129520097241 0.062500 0.0008287161516541 -0.250000 0.0132077483758496 1.000000 0.1984573362019444 1.250000 0.2985382323180470 2.000000 0.6467637282835621 -4.000000 1.0697266613089194 7.500000 0.3883130800042056 11.000000 0.7485424374510771 11.500000 0.8466485464256736 -16.000000 0.5838573246424439 20.000000 0.8060058452421577 25.000000 0.5388036213269295 -30.000000 0.7217503783469900 50.000000 0.5800784479454419 75.000000 0.6015191038544081 -80.000000 0.7061151114728683 100.000000 0.6163111032720134 -125.000000 0.6277848076544366 STRUVE_L0_VALUES_TEST: STRUVE_L0_VALUES stores values of the Struve L0 function. X L0(X) 0.001953 1.2433985199262821e-03 -0.031250 -1.9896526647882936e-02 0.125000 7.9715713253115009e-02 -0.500000 -3.2724069939418077e-01 1.000000 7.1024318593789093e-01 2.000000 1.9374337579914456e+00 -4.000000 -1.1131050203248584e+01 7.000000 1.6850062034703268e+02 -10.000000 -2.8156522493745947e+03 16.000000 8.9344618796978402e+05 16.250000 1.1382025002851451e+06 -17.000000 -2.3549701855860190e+06 20.000000 4.3558282527641043e+07 22.500000 4.9993516476037955e+08 -25.000000 -5.7745606064408045e+09 30.000000 7.8167229782395630e+11 -40.000000 -1.4894774793419900e+16 50.000000 2.9325537838493362e+20 60.000000 5.8940770556098012e+24 -70.000000 -1.2015889579125464e+29 STRUVE_L1_VALUES_TEST: STRUVE_L1_VALUES stores values of the Struve L1 function. X L1(X) 0.001953 8.0950410749865127e-07 -0.031250 2.0724649092571513e-04 0.125000 3.3191834066894515e-03 -0.500000 5.3942182623522662e-02 1.000000 2.2676438105580865e-01 2.000000 1.1027597873677157e+00 -4.000000 9.1692778117386844e+00 7.000000 1.5541656652426661e+02 -10.000000 2.6703582852084828e+03 16.000000 8.6505880175304634e+05 16.250000 1.1026046613094942e+06 -17.000000 2.2846209494153936e+06 20.000000 4.2454972750111982e+07 22.500000 4.8869614587997693e+08 -25.000000 5.6578651292431049e+09 30.000000 7.6853203893832104e+11 -40.000000 1.4707396163259352e+16 50.000000 2.9030785901035569e+20 60.000000 5.8447515883904678e+24 -70.000000 1.1929750788892311e+29 STUDENT_CDF_VALUES_TEST: STUDENT_CDF_VALUES returns values of the Student T Cumulative Density Function. C X STUDENT_CDF(A,X) 1.000000 0.325000 0.6000231200328521 2.000000 0.289000 0.6001080279134390 3.000000 0.277000 0.6001150934648930 4.000000 0.271000 0.6000995134721354 5.000000 0.267000 0.5999341989834830 2.000000 0.816000 0.7498859393137811 5.000000 0.727000 0.7500879487671045 2.000000 2.920000 0.9500004222186464 5.000000 2.015000 0.9499969138365968 2.000000 6.965000 0.9900012348724744 3.000000 4.541000 0.9900017619355059 4.000000 3.747000 0.9900004567580596 5.000000 3.365000 0.9900007637471291 STUDENT_NONCENTRAL_CDF_VALUES_TEST: STUDENT_NONCENTRAL_CDF_VALUES returns values of the noncentral Student T Cumulative Density Function. X LAMBDA DF CDF 3.000000 0.000000 1 0.8975836176504333 3.000000 0.000000 2 0.9522670169000000 3.000000 0.000000 3 0.9711655571887813 3.000000 0.500000 1 0.8231218863999999 3.000000 0.500000 2 0.9049021510000000 3.000000 0.500000 3 0.9363471834000000 3.000000 1.000000 1 0.7301025986000000 3.000000 1.000000 2 0.8335594263000000 3.000000 1.000000 3 0.8774010255000000 3.000000 2.000000 1 0.5248571617000000 3.000000 2.000000 2 0.6293856597000000 3.000000 2.000000 3 0.6800271741000000 3.000000 4.000000 1 0.2059013197500000 3.000000 4.000000 2 0.2112148916000000 3.000000 4.000000 3 0.2074730718000000 15.000000 7.000000 15 0.9981130072000000 15.000000 7.000000 20 0.9994873850000000 15.000000 7.000000 25 0.9998391562000000 0.050000 1.000000 1 0.1686105669720000 0.050000 1.000000 2 0.1696795098500000 0.050000 1.000000 3 0.1701041003000000 4.000000 2.000000 10 0.9247683363000000 4.000000 3.000000 10 0.7483139269000000 4.000000 4.000000 10 0.4659802096000000 5.000000 2.000000 10 0.9761872541000000 5.000000 3.000000 10 0.8979689357000000 5.000000 4.000000 10 0.7181904627000000 6.000000 2.000000 10 0.9923658945000000 6.000000 3.000000 10 0.9610341649000000 6.000000 4.000000 10 0.8688007350000000 SUBFACTORIAL_VALUES_TEST: SUBFACTORIAL_VALUES returns values of the subfactorial function. N Subfactorial(N) 0 1 1 0 2 1 3 2 4 9 5 44 6 265 7 1854 8 14833 9 133496 10 1334961 11 14684570 12 176214841 SURTEN_VALUES_TEST: SURTEN_VALUES stores values of the surface tension of water as a function of temperature. T SIGMA(T) 10.000000 74.2199999999999989 20.000000 72.7399999999999949 30.000000 71.2000000000000028 40.000000 69.5999999999999943 50.000000 67.9500000000000028 100.000000 58.9200000000000017 150.000000 48.7500000000000000 200.000000 37.6799999999999997 250.000000 26.0500000000000007 300.000000 14.3699999999999992 325.000000 8.7799999999999994 350.000000 3.6699999999999999 370.000000 0.4000000000000000 373.976000 0.0000000000000000 SYNCH1_VALUES_TEST: SYNCH1_VALUES stores values of the synchrotron function. X FX 0.001953 0.2651486454748740 0.031250 0.6205012997907905 0.125000 0.8511257213236801 0.500000 0.8708191468754688 1.000000 0.6514228153553639 1.500000 0.4506404092032236 2.000000 0.3016359028507394 2.500000 0.1981449080444131 3.000000 0.1285657100090638 4.000000 0.0528273966978668 4.250000 0.0421392984717203 5.000000 0.0212481297749820 5.500000 0.0134002589075055 6.000000 0.0084260797314109 8.000000 0.0012884516186755 10.000000 0.0001922382643009 12.000000 0.0000282210708340 15.000000 0.0000015548757973 20.000000 0.0000000119686345 25.000000 0.0000000000895642 SYNCH2_VALUES_TEST: SYNCH2_VALUES stores values of the synchrotron function. X FX 0.001953 0.1343072727566738 0.031250 0.3348526527242418 0.125000 0.5040422411091108 0.500000 0.6029652323601679 1.000000 0.4944750621042083 1.500000 0.3603606786047336 2.000000 0.2496778549762566 2.500000 0.1681383054290583 3.000000 0.1111712234855655 4.000000 0.0469232058261013 4.250000 0.0376245458619800 5.000000 0.0192221231724841 5.500000 0.0122095353436547 6.000000 0.0077249644268526 8.000000 0.0012029044213679 10.000000 0.0001816118756953 12.000000 0.0000268843380066 15.000000 0.0000014942212731 20.000000 0.0000000116076969 25.000000 0.0000000000873623 TAN_VALUES_TEST: TAN_VALUES stores values of the tangent function. X FX 0.000000 0.0000000000000000 0.261799 0.2679491924311227 0.500000 0.5463024898437905 0.523599 0.5773502691896257 0.785398 1.0000000000000000 1.000000 1.5574077246549023 1.047198 1.7320508075688772 1.308997 3.7320508075688772 1.439897 7.5957541127251504 1.505346 15.2570516882655394 2.000000 -2.1850398632615189 3.000000 -0.1425465430742778 3.141593 0.0000000000000000 4.000000 1.1578212823495775 5.000000 -3.3805150062465859 TANH_VALUES_TEST: TANH_VALUES stores values of the hyperbolic tangent function. X FX -5.000000 -0.9999092042625951 -1.000000 -0.7615941559557649 0.000000 0.0000000000000000 0.100000 0.0996679946249558 0.200000 0.1973753202249040 0.300000 0.2913126124515909 0.400000 0.3799489622552249 0.500000 0.4621171572600097 0.600000 0.5370495669980353 0.700000 0.6043677771171635 0.800000 0.6640367702678490 0.900000 0.7162978701990245 1.000000 0.7615941559557649 2.000000 0.9640275800758169 3.000000 0.9950547536867305 4.000000 0.9993292997390670 5.000000 0.9999092042625951 10.000000 0.9999999958776927 TAU_VALUES_TEST: TAU_VALUES returns values of the TAU function. N TAU(N) 1 1 2 2 3 2 4 3 5 2 6 4 7 2 8 4 9 3 10 4 23 2 72 12 126 12 226 4 300 18 480 24 521 2 610 8 832 14 960 28 THERCON_VALUES_TEST: THERCON_VALUES stores values of the thermal conductivity of water as a function of temperature and pressure. T P LAMBDA(T,P) 0.000000 1.000000 561.0000000000000000 0.000000 5.000000 561.2999999999999545 0.000000 10.000000 561.5000000000000000 0.000000 25.000000 562.3999999999999773 0.000000 50.000000 563.7000000000000455 0.000000 75.000000 565.1000000000000227 0.000000 100.000000 566.5000000000000000 0.000000 125.000000 567.8999999999999773 0.000000 150.000000 569.2999999999999545 0.000000 175.000000 570.6000000000000227 0.000000 200.000000 572.0000000000000000 0.000000 225.000000 573.3999999999999773 0.000000 250.000000 574.7999999999999545 0.000000 275.000000 576.1000000000000227 0.000000 300.000000 577.5000000000000000 0.000000 350.000000 580.2000000000000455 0.000000 400.000000 582.8999999999999773 0.000000 450.000000 585.5000000000000000 0.000000 500.000000 588.1000000000000227 0.000000 550.000000 590.7000000000000455 0.000000 600.000000 593.2999999999999545 0.000000 650.000000 595.7999999999999545 0.000000 700.000000 598.2999999999999545 0.000000 800.000000 603.1000000000000227 0.000000 900.000000 607.7999999999999545 0.000000 1000.000000 612.2000000000000455 25.000000 1.000000 607.2000000000000455 50.000000 1.000000 643.6000000000000227 75.000000 1.000000 666.7999999999999545 100.000000 1.000000 25.0799999999999983 150.000000 1.000000 28.8500000000000014 200.000000 1.000000 33.2800000000000011 400.000000 1.000000 54.7599999999999980 600.000000 1.000000 79.8900000000000006 800.000000 1.000000 107.2999999999999972 THREE_J_VALUES_TEST: THREE_J_VALUES returns values of the Wigner 3J coefficient. J1 J2 J3 M1 M2 M3 THREE_J 1.00 4.50 3.50 1.00 -3.50 2.50 0.2788866755113585 2.00 4.50 3.50 1.00 -3.50 2.50 -0.0953462589245592 3.00 4.50 3.50 1.00 -3.50 2.50 -0.0674199862463242 4.00 4.50 3.50 1.00 -3.50 2.50 0.1533110351679666 5.00 4.50 3.50 1.00 -3.50 2.50 -0.1564465546936860 6.00 4.50 3.50 1.00 -3.50 2.50 0.1099450412156551 7.00 4.50 3.50 1.00 -3.50 2.50 -0.0553623569313172 8.00 4.50 3.50 1.00 -3.50 2.50 0.0179983545113779 TRAN02_VALUES_TEST: TRAN02_VALUES stores values of the transportation function of order 2. X FX 0.001953 0.0019531247930395 0.031250 0.0312491523143311 0.125000 0.1249457719478345 0.500000 0.4965536361564060 1.000000 0.9730325613551701 1.500000 1.4121978695932527 2.000000 1.8017185674405778 2.500000 2.1350385339277045 3.000000 2.4110500490169535 4.000000 2.8066664045631180 4.250000 2.8777421863296233 5.000000 3.0391706043438553 5.500000 3.1125074928667358 6.000000 3.1656687817738578 8.000000 3.2623520367816008 10.000000 3.2843291144979516 15.000000 3.2897895167775788 20.000000 3.2898672226665502 30.000000 3.2898681336064324 50.000000 3.2898681336964528 TRAN03_VALUES_TEST: TRAN03_VALUES stores values of the transportation function of order 3. X FX 0.001953 0.0000019073483296 0.031250 0.0004882613824318 0.125000 0.0078074163848431 0.500000 0.1237086871881203 1.000000 0.4798410065724175 1.500000 1.0269431622039755 2.000000 1.7063547219458659 2.500000 2.4539217444475936 3.000000 3.2106046629422469 4.000000 4.5792174372291568 4.250000 4.8722022832940368 5.000000 5.6143866138422736 5.500000 5.9984455864575468 6.000000 6.3033953673480960 8.000000 6.9579908688361165 10.000000 7.1503227120085926 15.000000 7.2110731475871876 20.000000 7.2123221966388460 30.000000 7.2123414161609469 50.000000 7.2123414189575659 TRAN04_VALUES_TEST: TRAN04_VALUES stores values of the transportation function of order 4. X FX 0.001953 0.0000000024835264 0.031250 0.0000101720293536 0.125000 0.0006505333240594 0.500000 0.0411504480041557 1.000000 0.3172440452344265 1.500000 1.0079442901142373 2.000000 2.2010881024333409 2.500000 3.8846508619156546 3.000000 5.9648223973714769 4.000000 10.7319323929986226 4.250000 11.9400288768193654 5.000000 15.3597843168821822 5.500000 17.3725876330937439 6.000000 19.1229760160531654 8.000000 23.5839791569219415 10.000000 25.2736676770304420 15.000000 25.9551982145722562 20.000000 25.9753509352122407 30.000000 25.9757575220840948 50.000000 25.9757576090673155 TRAN05_VALUES_TEST: TRAN05_VALUES stores values of the transportation function of order 5. X FX 0.001953 0.0000000000036380 0.031250 0.0000002384056445 0.125000 0.0000609822053722 0.500000 0.0154100045863767 1.000000 0.2366158792390948 1.500000 1.1198756851307630 2.000000 3.2292901663684050 2.500000 7.0362973105160656 3.000000 12.7705576910441589 4.000000 29.4883390152458453 4.250000 34.4713405403622559 5.000000 50.2630922181751885 5.500000 60.8199091011271662 6.000000 70.8733344292134575 8.000000 101.4778124297778845 10.000000 116.3807454024207146 15.000000 124.0962390126296810 20.000000 124.4227015563255065 30.000000 124.4313279083858959 50.000000 124.4313306172043241 TRAN06_VALUES_TEST: TRAN06_VALUES stores values of the transportation function of order 6. X FX 0.001953 0.0000000000000057 0.031250 0.0000000059601180 0.125000 0.0000060978424398 0.500000 0.0061578909866319 1.000000 0.1885436027568084 1.500000 1.3319251347921659 2.000000 5.0857202271697615 2.500000 13.7292223654665566 3.000000 29.5795924816414413 4.000000 88.6008357068998578 4.250000 109.1603711337300524 5.000000 182.2432374957535899 5.500000 237.6538312558675727 6.000000 295.4324674595937950 8.000000 506.8124438128045313 10.000000 638.7823113494612244 15.000000 726.9920355699487118 20.000000 732.3033164314684882 30.000000 732.4869201588209080 50.000000 732.4870046287999230 TRAN07_VALUES_TEST: TRAN07_VALUES stores values of the transportation function of order 7. X FX 0.001953 0.0000000000000000 0.031250 0.0000000001552110 0.125000 0.0000006351623837 0.500000 0.0025638801246626 1.000000 0.1566532899381165 1.500000 1.6538225039181098 2.000000 8.3763085709508207 2.500000 28.0785707178307646 3.000000 72.0096760467519914 4.000000 281.7490570169190960 4.250000 366.6022797532779123 5.000000 705.5606798260359938 5.500000 996.6192756275562488 6.000000 1328.8914430417403310 8.000000 2798.7640273169131433 10.000000 3972.1376409416502611 15.000000 4991.3492839319897030 20.000000 5078.1562639825015140 30.000000 5082.0777202028712054 50.000000 5082.0803580047167998 TRAN08_VALUES_TEST: TRAN08_VALUES stores values of the transportation function of order 8. X FX 0.001953 0.0000000000000000 0.031250 0.0000000000041574 0.125000 0.0000000680506512 0.500000 0.0010981703519563 1.000000 0.1339643277618788 1.500000 2.1153387806998616 2.000000 14.2278770287507363 2.500000 59.3120614316478409 3.000000 181.3961457704314739 4.000000 931.4800192899222111 4.250000 1281.7928112604611215 5.000000 2857.2838386329240166 5.500000 4387.2971687877734439 6.000000 6299.3229139406657850 8.000000 16589.4262771548892488 10.000000 27064.7807987973974377 15.000000 38974.5560625436628470 20.000000 40400.2407169050275115 30.000000 40484.3165041206520982 50.000000 40484.3990018921831506 TRAN09_VALUES_TEST: TRAN09_VALUES stores values of the transportation function of order 9. X FX 0.001953 0.0000000000000000 0.031250 0.0000000000001137 0.125000 0.0000000074428246 0.500000 0.0004802272848542 1.000000 0.1170024301435868 1.500000 2.7648973910899914 2.000000 24.7166314058291938 2.500000 128.2711982884982831 3.000000 468.4289480066220790 4.000000 3167.3967371627895773 4.250000 4614.0886546630199518 5.000000 11952.7185453923029854 5.500000 20001.6126664770272328 6.000000 31011.0732718513681903 8.000000 103529.4990554113028338 10.000000 197431.7301714059140068 15.000000 338260.3041465845890343 20.000000 361796.0703675075783394 30.000000 363606.2212477755965665 50.000000 363608.8055882716435008 TRIGAMMA_VALUES_TEST: TRIGAMMA_VALUES stores values of the TriGamma function. X FX 1.000000 1.6449340668482260 1.100000 1.4332991507927590 1.200000 1.2673772054237791 1.300000 1.1342534349966189 1.400000 1.0253565905295969 1.500000 0.9348022005446793 1.600000 0.8584318931245799 1.700000 0.7932328301639984 1.800000 0.7369741375017002 1.900000 0.6879720582426356 2.000000 0.6449340668482264 TRUNCATED_NORMAL_AB_CDF_VALUES_TEST: TRUNCATED_NORMAL_AB_CDF_VALUES stores values of the CDF of the Normal Distribution truncated to [A,B]. MU SIGMA A B X FX 100.000000 25.000000 50.000000 150.000000 90.000000 0.3371694242213513 100.000000 25.000000 50.000000 150.000000 92.000000 0.3685009225506048 100.000000 25.000000 50.000000 150.000000 94.000000 0.4006444233448185 100.000000 25.000000 50.000000 150.000000 96.000000 0.4334107066903040 100.000000 25.000000 50.000000 150.000000 98.000000 0.4665988676496338 100.000000 25.000000 50.000000 150.000000 100.000000 0.5000000000000000 100.000000 25.000000 50.000000 150.000000 102.000000 0.5334011323503662 100.000000 25.000000 50.000000 150.000000 104.000000 0.5665892933096960 100.000000 25.000000 50.000000 150.000000 106.000000 0.5993555766551815 100.000000 25.000000 50.000000 150.000000 108.000000 0.6314990774493952 100.000000 25.000000 50.000000 150.000000 110.000000 0.6628305757786487 TRUNCATED_NORMAL_AB_PDF_VALUES_TEST: TRUNCATED_NORMAL_AB_PDF_VALUES stores values of the PDF of the Normal Distribution truncated to [A,B]. MU SIGMA A B X FX 100.000000 25.000000 50.000000 150.000000 90.000000 0.0154330117180184 100.000000 25.000000 50.000000 150.000000 92.000000 0.0158839447227064 100.000000 25.000000 50.000000 150.000000 94.000000 0.0162437599703192 100.000000 25.000000 50.000000 150.000000 96.000000 0.0165057504646926 100.000000 25.000000 50.000000 150.000000 98.000000 0.0166649686938595 100.000000 25.000000 50.000000 150.000000 100.000000 0.0167183820094054 100.000000 25.000000 50.000000 150.000000 102.000000 0.0166649686938595 100.000000 25.000000 50.000000 150.000000 104.000000 0.0165057504646926 100.000000 25.000000 50.000000 150.000000 106.000000 0.0162437599703192 100.000000 25.000000 50.000000 150.000000 108.000000 0.0158839447227064 100.000000 25.000000 50.000000 150.000000 110.000000 0.0154330117180184 TRUNCATED_NORMAL_A_CDF_VALUES_TEST: TRUNCATED_NORMAL_A_CDF_VALUES stores values of the CDF of the Normal Distribution truncated to [A,+oo). MU SIGMA A X FX 100.000000 25.000000 50.000000 90.000000 0.3293202045481688 100.000000 25.000000 50.000000 92.000000 0.3599223134505957 100.000000 25.000000 50.000000 94.000000 0.3913175216041539 100.000000 25.000000 50.000000 96.000000 0.4233210140873113 100.000000 25.000000 50.000000 98.000000 0.4557365629792204 100.000000 25.000000 50.000000 100.000000 0.4883601253415709 100.000000 25.000000 50.000000 102.000000 0.5209836877039214 100.000000 25.000000 50.000000 104.000000 0.5533992365958303 100.000000 25.000000 50.000000 106.000000 0.5854027290789878 100.000000 25.000000 50.000000 108.000000 0.6167979372325459 100.000000 25.000000 50.000000 110.000000 0.6474000461349729 TRUNCATED_NORMAL_A_PDF_VALUES_TEST: TRUNCATED_NORMAL_A_PDF_VALUES stores values of the PDF of the Normal Distribution truncated to [A,+oo). MU SIGMA A X FX 100.000000 25.000000 50.000000 90.000000 0.0150737350740188 100.000000 25.000000 50.000000 92.000000 0.0155141704713989 100.000000 25.000000 50.000000 94.000000 0.0158656093102469 100.000000 25.000000 50.000000 96.000000 0.0161215007315879 100.000000 25.000000 50.000000 98.000000 0.0162770124002932 100.000000 25.000000 50.000000 100.000000 0.0163291822672430 100.000000 25.000000 50.000000 102.000000 0.0162770124002932 100.000000 25.000000 50.000000 104.000000 0.0161215007315879 100.000000 25.000000 50.000000 106.000000 0.0158656093102469 100.000000 25.000000 50.000000 108.000000 0.0155141704713989 100.000000 25.000000 50.000000 110.000000 0.0150737350740188 TRUNCATED_NORMAL_B_CDF_VALUES_TEST: TRUNCATED_NORMAL_B_CDF_VALUES stores values of the CDF of the Normal Distribution truncated to (-oo,B]. MU SIGMA B X FX 100.000000 25.000000 150.000000 90.000000 0.3525999538650271 100.000000 25.000000 150.000000 92.000000 0.3832020627674540 100.000000 25.000000 150.000000 94.000000 0.4145972709210122 100.000000 25.000000 150.000000 96.000000 0.4466007634041696 100.000000 25.000000 150.000000 98.000000 0.4790163122960786 100.000000 25.000000 150.000000 100.000000 0.5116398746584291 100.000000 25.000000 150.000000 102.000000 0.5442634370207796 100.000000 25.000000 150.000000 104.000000 0.5766789859126887 100.000000 25.000000 150.000000 106.000000 0.6086824783958461 100.000000 25.000000 150.000000 108.000000 0.6400776865494043 100.000000 25.000000 150.000000 110.000000 0.6706797954518312 TRUNCATED_NORMAL_B_PDF_VALUES_TEST: TRUNCATED_NORMAL_B_PDF_VALUES stores values of the PDF of the Normal Distribution truncated to (-oo,B]. MU SIGMA B X FX 100.000000 25.000000 150.000000 90.000000 0.0150737350740188 100.000000 25.000000 150.000000 92.000000 0.0155141704713989 100.000000 25.000000 150.000000 94.000000 0.0158656093102469 100.000000 25.000000 150.000000 96.000000 0.0161215007315879 100.000000 25.000000 150.000000 98.000000 0.0162770124002932 100.000000 25.000000 150.000000 100.000000 0.0163291822672430 100.000000 25.000000 150.000000 102.000000 0.0162770124002932 100.000000 25.000000 150.000000 104.000000 0.0161215007315879 100.000000 25.000000 150.000000 106.000000 0.0158656093102469 100.000000 25.000000 150.000000 108.000000 0.0155141704713989 100.000000 25.000000 150.000000 110.000000 0.0150737350740188 TSAT_VALUES_TEST: TSAT_VALUES stores values of the saturation temperature as a function of pressure. P Tsat(P) 0.006117 0.0100000000000000 0.012000 9.6549999999999994 0.025000 21.0799999999999983 0.055000 34.5889999999999986 0.080000 41.5180000000000007 0.110000 47.6950000000000003 0.160000 55.3269999999999982 0.250000 64.9800000000000040 0.500000 81.3389999999999986 0.750000 91.7830000000000013 1.000000 99.6320000000000050 1.500000 111.3780000000000001 2.000000 120.4429999999999978 5.000000 151.8660000000000139 10.000000 179.9159999999999968 20.000000 212.4170000000000016 50.000000 263.9769999999999754 100.000000 311.0310000000000059 200.000000 365.8000000000000114 220.550000 373.9759999999999991 VAN_DER_CORPUT_VALUES_TEST: VAN_DER_CORPUT_VALUES stores values of the van der Corput sequence in a given base. BASE SEED VDC(BASE,SEED) 2 0 0.0000000000000000e+00 2 1 5.0000000000000000e-01 2 2 2.5000000000000000e-01 2 3 7.5000000000000000e-01 2 4 1.2500000000000000e-01 2 5 6.2500000000000000e-01 2 6 3.7500000000000000e-01 2 7 8.7500000000000000e-01 2 8 6.2500000000000000e-02 3 0 0.0000000000000000e+00 3 1 3.3333333333333331e-01 3 2 6.6666666666666663e-01 3 3 1.1111111111111110e-01 3 4 4.4444444444444442e-01 3 5 7.7777777777777768e-01 3 6 2.2222222222222221e-01 3 7 5.5555555555555558e-01 3 8 8.8888888888888884e-01 4 0 0.0000000000000000e+00 4 1 2.5000000000000000e-01 4 2 5.0000000000000000e-01 4 3 7.5000000000000000e-01 4 4 6.2500000000000000e-02 4 5 3.1250000000000000e-01 4 6 5.6250000000000000e-01 4 7 8.1250000000000000e-01 4 8 1.2500000000000000e-01 2 10 3.1250000000000000e-01 3 10 3.7037037037037029e-01 4 10 6.2500000000000000e-01 5 10 8.0000000000000002e-02 7 10 4.4897959183673469e-01 11 10 9.0909090909090917e-01 13 10 7.6923076923076927e-01 2 100 1.4843750000000000e-01 3 100 4.1152263374485593e-01 4 100 9.7656250000000000e-02 5 100 3.2000000000000001e-02 7 100 2.9154518950437308e-01 11 100 1.6528925619834711e-01 13 100 7.3372781065088755e-01 2 1000 9.2773437500000000e-02 3 1000 3.4750800182898950e-01 4 1000 1.7089843750000000e-01 5 1000 5.1200000000000004e-03 7 1000 9.1628488129945862e-01 11 1000 9.3163035311795650e-01 13 1000 9.9044151115157042e-01 2 10000 3.4729003906250000e-02 3 10000 3.8612000203221047e-01 4 10000 1.8920898437500000e-02 5 10000 5.1199999999999998e-04 7 10000 5.7499851252454326e-01 11 10000 1.5299501400177579e-01 13 10000 2.4592976436399289e-01 29 1000 4.8874492599122549e-01 29 1001 5.2322768461191527e-01 29 1002 5.5771044323260488e-01 29 1003 5.9219320185329449e-01 29 1004 6.2667596047398422e-01 71 1000 8.7284268994247197e-02 71 1001 1.0136877603650070e-01 71 1002 1.1545328307875420e-01 71 1003 1.2953779012100769e-01 71 1004 1.4362229716326130e-01 173 1000 7.8051388285609280e-01 173 1001 7.8629422967690199e-01 173 1002 7.9207457649771129e-01 173 1003 7.9785492331852048e-01 173 1004 8.0363527013932978e-01 409 1000 4.4499973099156509e-01 409 1001 4.4744471876662623e-01 409 1002 4.4988970654168742e-01 409 1003 4.5233469431674839e-01 409 1004 4.5477968209180958e-01 VISCOSITY_VALUES_TEST: VISCOSITY_VALUES stores values of the viscosity of water as a function of temperature and pressure. T P ETA(T,P) 0.000000 1.000000 1792.0000000000000000 0.000000 5.000000 1791.0000000000000000 0.000000 10.000000 1790.0000000000000000 0.000000 25.000000 1786.0000000000000000 0.000000 50.000000 1780.0000000000000000 0.000000 75.000000 1775.0000000000000000 0.000000 100.000000 1769.0000000000000000 0.000000 125.000000 1764.0000000000000000 0.000000 150.000000 1759.0000000000000000 0.000000 175.000000 1754.0000000000000000 0.000000 200.000000 1749.0000000000000000 0.000000 225.000000 1744.0000000000000000 0.000000 250.000000 1739.0000000000000000 0.000000 275.000000 1735.0000000000000000 0.000000 300.000000 1731.0000000000000000 0.000000 350.000000 1722.0000000000000000 0.000000 400.000000 1714.0000000000000000 0.000000 450.000000 1707.0000000000000000 0.000000 500.000000 1700.0000000000000000 0.000000 550.000000 1694.0000000000000000 0.000000 600.000000 1687.0000000000000000 0.000000 650.000000 1682.0000000000000000 0.000000 700.000000 1676.0000000000000000 0.000000 800.000000 1667.0000000000000000 0.000000 900.000000 1659.0000000000000000 0.000000 1000.000000 1653.0000000000000000 25.000000 1.000000 890.7999999999999545 50.000000 1.000000 547.1000000000000227 75.000000 1.000000 378.3999999999999773 100.000000 1.000000 12.2799999999999994 200.000000 1.000000 16.1799999999999997 400.000000 1.000000 24.4499999999999993 600.000000 1.000000 32.6099999999999994 800.000000 1.000000 40.3800000000000026 VON_MISES_CDF_VALUES_TEST: VON_MISES_CDF_VALUES stores values of the von Mises CDF. A B X FX 0.000000 1.000000 -2.617994 0.0253508995628118 0.000000 1.000000 -1.570796 0.1097539041177346 0.000000 1.000000 0.000000 0.5000000000000000 0.000000 1.000000 1.047198 0.8043381312498558 0.000000 1.000000 2.094395 0.9417460124555197 1.000000 2.000000 1.000000 0.5000000000000000 1.000000 2.000000 1.200000 0.6018204118446155 1.000000 2.000000 1.400000 0.6959356933122230 1.000000 2.000000 1.600000 0.7765935901304593 1.000000 2.000000 1.800000 0.8410725934916615 1.000000 2.000000 2.000000 0.8895777369550366 -2.000000 3.000000 0.000000 0.9960322705517926 -1.000000 3.000000 0.000000 0.9404336090170247 0.000000 3.000000 0.000000 0.5000000000000000 1.000000 3.000000 0.000000 0.0595663909829753 2.000000 3.000000 0.000000 0.0039677294482076 3.000000 3.000000 0.000000 0.0002321953958112 0.000000 0.000000 0.785398 0.6250000000000000 0.000000 1.000000 0.785398 0.7438406999109122 0.000000 2.000000 0.785398 0.8369224904294019 0.000000 3.000000 0.785398 0.8941711407897124 0.000000 4.000000 0.785398 0.9291058600568743 0.000000 5.000000 0.785398 0.9514289900655436 WEEKDAY_VALUES_TEST: WEEKDAY_VALUES stores values of the weekday for a given Y/M/D date. Y M D W -587 7 30 1 -169 12 8 4 70 9 26 4 135 10 3 1 470 1 7 4 576 5 18 2 694 11 7 7 1013 4 19 1 1066 10 14 7 1096 5 18 1 1190 3 16 6 1240 3 3 7 1288 3 26 6 1298 4 20 1 1391 6 4 1 1436 1 25 4 1492 3 31 7 1553 9 9 7 1560 2 24 7 1648 6 10 4 1680 6 30 1 1716 7 24 6 1768 6 19 1 1819 8 2 2 1839 3 27 4 1903 4 19 1 1929 8 25 1 1941 9 29 2 1943 4 19 2 1943 10 7 5 1992 3 17 3 1996 2 25 1 2038 11 10 4 2094 7 18 1 WEIBULL_CDF_VALUES_TEST: WEIBULL_CDF_VALUES stores values of the Weibull Cumulative Density Function. Alpha Beta X CDF(X) 1.000000 0.500000 1.000000 0.8646647167633873 1.000000 0.500000 2.000000 0.9816843611112658 1.000000 0.500000 3.000000 0.9975212478233336 1.000000 0.500000 4.000000 0.9996645373720975 1.000000 2.000000 2.000000 0.6321205588285577 1.000000 3.000000 2.000000 0.4865828809674080 1.000000 4.000000 2.000000 0.3934693402873666 1.000000 5.000000 2.000000 0.3296799539643607 2.000000 2.000000 3.000000 0.8946007754381357 3.000000 2.000000 3.000000 0.9657818816883340 4.000000 2.000000 3.000000 0.9936702845725143 5.000000 2.000000 3.000000 0.9994964109502630 WRIGHT_OMEGA_VALUES_TEST: WRIGHT_OMEGA_VALUES stores values of the Wright Omega function. Z FZ 0 0 0.5671432904097838 0 0 0 0 0 1 0 1 0 0 0 0 0 3.71828 0 2.718281828459045 0 0 0 0 0 -1 0 -1 0 0 3.14159 0 0 -1 0 -1 0 -0 -3.14159 0 0 ZETA_VALUES_TEST: ZETA_VALUES returns values of the Riemann Zeta function. N Zeta(N) 2 1.6449340668482264 3 1.2020569031595942 4 1.0823232337111381 5 1.0369277551433700 6 1.0173430619844492 7 1.0083492773819229 8 1.0040773561979444 9 1.0020083929260821 10 1.0009945751278180 11 1.0004941886041194 12 1.0002460865533080 16 1.0000152822594086 20 1.0000009539620338 30 1.0000000009313275 40 1.0000000000009095 ZETA_M1_VALUES_TEST: ZETA_M1_VALUES returns values of the Riemann Zeta Minus One function. N Zeta_M1(N) 2.00 0.6449340668482264 2.50 0.3414872573000000 3.00 0.2020569031595943 3.50 0.1267338673000000 4.00 0.0823232337111382 5.00 0.0369277551433699 6.00 0.0173430619844491 7.00 0.0083492773819228 8.00 0.0040773561979443 9.00 0.0020083929260822 10.00 0.0009945751278181 11.00 0.0004941886041195 12.00 0.0002460865533080 16.00 0.0000152822594087 20.00 0.0000009539620339 30.00 0.0000000000931327 40.00 0.0000000000009095 TEST_VALUES_TEST Normal end of execution. 23-Jun-2018 08:47:33 exit