28 December 2023 2:12:23.625 PM test_values_test(): FORTRAN90 version Test test_values(). abram0_values_test(): abram0_values() returns values of the Abramowitz function of order 0 X Abram0 0.195312E-02 0.8737772630698536 0.781250E-02 0.8472185965045692 0.312500E-01 0.7728893448398830 0.125000 0.5968434585345015 0.500000 0.2987173528367589 1.00000 0.1500459645051639 1.25000 0.1111466241915796 1.50000 0.8390956715315190E-01 1.87500 0.5655232171794342E-01 2.00000 0.4987649660303379E-01 2.12500 0.4410088921976279E-01 3.00000 0.1973853518025406E-01 4.00000 0.8619308828716149E-02 5.00000 0.4022478816254013E-02 6.00000 0.1971865845816489E-02 7.00000 0.1004586834013354E-02 10.0000 0.1572691726330450E-03 15.0000 0.1035266691235026E-04 20.0000 0.9122975919095675E-06 40.0000 0.2562828773795270E-09 ABRAM1_VALUES_TEST: ABRAM1_VALUES returns values of the Abramowitz function of order 1 X Abram1 0.195312E-02 0.4982821984879992 0.781250E-02 0.4932439177304729 0.312500E-01 0.4743161278469123 0.125000 0.4109598325876041 0.500000 0.2531761738822704 1.00000 0.1465633813859778 1.25000 0.1142154705601837 1.50000 0.9002630738348376E-01 1.87500 0.6408821417074230E-01 2.00000 0.5744661431416619E-01 2.12500 0.5158162456480073E-01 3.00000 0.2526371955577641E-01 4.00000 0.1193080333019659E-01 5.00000 0.5927054228091528E-02 6.00000 0.3060921535801783E-02 7.00000 0.1630738213697955E-02 10.0000 0.2837185191695945E-03 15.0000 0.2112215012132324E-04 20.0000 0.2034457889260163E-05 40.0000 0.7111651723620965E-09 ABRAM2_VALUES_TEST: ABRAM2_VALUES returns values of the Abramowitz function of order 2 X Abram2 0.195312E-02 0.4421385816210791 0.781250E-02 0.4392337954568403 0.312500E-01 0.4278985729709260 0.125000 0.3865282566185451 0.500000 0.2653820441323137 1.00000 0.1684873483833459 1.25000 0.1360920003251323 1.50000 0.1107033002772792 1.87500 0.8212601999553039E-01 2.00000 0.7453878199959459E-01 2.12500 0.6773203437761281E-01 3.00000 0.3564180869881185E-01 4.00000 0.1795658995661827E-01 5.00000 0.9405873714357537E-02 6.00000 0.5080935620429921E-02 7.00000 0.2814956541420972E-02 10.0000 0.5380869642255930E-03 15.0000 0.4482175638014632E-04 20.0000 0.4689067842732410E-05 40.0000 0.2016154485099642E-08 AGM_VALUES_TEST: AGM_VALUES returns values of the arithmetic geometric mean function. A B AGM(A,B) 22.0000 96.0000 52.27464119870424 83.0000 56.0000 68.83653005985852 42.0000 7.00000 20.65930119673401 26.0000 11.0000 17.69685487374365 4.00000 63.0000 23.86704972175330 6.00000 45.0000 20.71701598280599 40.0000 75.0000 56.12784225561668 80.0000 0.00000 0.000000000000000 90.0000 35.0000 59.26956508122964 9.00000 1.00000 3.936235503649555 53.0000 53.0000 53.00000000000000 1.00000 2.00000 1.456791031046907 1.00000 4.00000 2.243028580287603 1.00000 8.00000 3.615756177597363 1.50000 8.00000 4.081692408022163 AIRY_AI_VALUES_TEST: AIRY_AI_VALUES returns values of the Airy function Ai(X) X Ai 0.00000 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 1.00000 0.1352924163128814 AIRY_AI_INT_VALUES_TEST: AIRY_AI_INT_VALUES returns values of the integral of the Airy function Ai(X) X Ai_Int -12.0000 -0.7522883891661012 -11.0000 -0.5734835018585489 -10.0000 -0.7656984031342129 -9.50000 -0.6518101550538247 -9.00000 -0.5588197489447188 -6.50000 -0.5690235287071681 -4.00000 -0.4780074964292617 -1.00000 -0.4656739834670686 -0.250000 -0.9678314094561802E-01 -0.976562E-03 -0.3468304985703561E-03 0.976562E-03 0.3465836691792793E-03 0.781250E-02 0.2765758184605123E-02 0.500000 0.1459533049118572 1.00000 0.2363173419171098 4.00000 0.3328926453861221 4.50000 0.3331875912977942 6.00000 0.3333294517052385 8.00000 0.3333333172424836 10.0000 0.3333333332991690 12.0000 0.3333333333332938 AIRY_AI_PRIME_VALUES_TEST: AIRY_AI_PRIME_VALUES returns values of the derivative of the Airy functions A'(X). X AiP 0.00000 -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 1.00000 -0.1591474412967932 AIRY_BI_VALUES_TEST: AIRY_BI_VALUES returns values of the Airy function Bi(X). X Bi 0.00000 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 1.042422171231561 0.900000 1.119872813134447 1.00000 1.207423594952871 AIRY_BI_INT_VALUES_TEST: AIRY_BI_INT_VALUES returns values of the integral of the Airy function Bi(X) X Bi_Int -12.0000 0.1766081903155463E-01 -10.0000 -0.1504042480614002E-01 -8.00000 0.1475644629322766E-01 -7.50000 -0.1184730426484845 -7.00000 -0.6491674126616585E-01 -6.50000 0.9726083246438104E-01 -4.00000 0.5076005849528754E-01 -1.00000 -0.3730050096342949 -0.250000 -0.1396298844266658 -0.195312E-02 -0.1200173526672330E-02 0.195312E-02 0.1201883611789035E-02 0.500000 0.3653384655095201 1.00000 0.8727691167380082 4.00000 48.21947526380343 8.00000 440065.2580490418 8.50000 1760815.397622830 9.00000 7377921.170522001 10.0000 147809803.1074067 12.0000 97037614223.61343 14.0000 116327376388098.8 AIRY_BI_PRIME_VALUES_TEST: AIRY_BI_PRIME_VALUES returns values of the Airy function derivative B'(X). X BiP 0.00000 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 1.00000 0.9324359333927756 AIRY_CAI_VALUES_TEST: AIRY_CAI_VALUES returns values of the Airy function Ai(X) with complex argument X Ai 1.00000 0.00000 0.1352924163128814 0.000000000000000 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 -0.8154602160771214E-01 -1.00000 0.00000 0.5355608832923521 0.000000000000000 -0.809017 -0.587785 0.5983692170633874 0.8154602160771214E-01 -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 returns values of the Airy function Bi(X) with complex argument X Bi 1.00000 0.00000 1.207423594952871 0.000000000000000 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 -1.00000 0.00000 0.1039973894969446 0.000000000000000 -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 returns values of the modified Airy function Gi(X). X Gi -0.195312E-02 0.2046830807004054 -0.125000 0.1837466283255790 -1.00000 -0.1166722172960153 -4.00000 0.3146693490272956 -8.00000 -0.3708904072242626 -8.25000 -0.2529305977242402 -9.00000 0.2896741065869270 -10.0000 -0.3464483649263409 -11.0000 0.2807603591387305 -13.0000 0.2181499450809486 0.195312E-02 0.2052667900081050 0.125000 0.2212369536378477 1.00000 0.2352184398104379 4.00000 0.8283430336376874E-01 7.00000 0.4575738549098928E-01 7.25000 0.4415001201460516E-01 8.00000 0.3995113371950891E-01 9.00000 0.3546770683394967E-01 10.0000 0.3189600510067959E-01 12.0000 0.2655689271351241E-01 AIRY_HI_VALUES_TEST: AIRY_HI_VALUES returns values of the modified Airy function Hi(X). X Hi -0.195312E-02 0.4093679827845889 -0.125000 0.3749529160804887 -1.00000 0.2206696067929599 -4.00000 0.7756535667970371E-01 -8.00000 0.3963882647312472E-01 -8.25000 0.3845007257500415E-01 -9.00000 0.3527321686831790E-01 -10.0000 0.3176853528250227E-01 -11.0000 0.2889440828805139E-01 -13.0000 0.2446328401167854E-01 0.195312E-02 0.4105354013999894 0.125000 0.4499350238120499 1.00000 0.9722051551424333 4.00000 83.76423710510437 7.00000 80327.74495204476 7.25000 155141.3884774911 8.00000 1199585.964173326 9.00000 21472868.85596764 10.0000 455641153.5163291 12.0000 329807225829.0476 ARCCOS_VALUES_TEST: ARCCOS_VALUES returns values of the arc cosine X F(X) -0.100000 1.670963747956457 0.00000 1.570796326794897 0.100000 1.470628905633337 0.200000 1.369438406004566 0.300000 1.266103672779499 0.400000 1.159279480727408 0.500000 1.047197551196598 0.600000 0.9272952180016122 0.700000 0.7953988301841436 0.800000 0.6435011087932844 0.900000 0.4510268117962624 1.00000 0.000000000000000 ARCCOSH_VALUES_TEST: ARCCOSH_VALUES returns values of the hyperbolic arc cosine X F(X) 1.00000 0.000000000000000 1.01000 0.1413037694856486 1.10000 0.4435682543851152 1.20000 0.6223625037147786 1.30000 0.7564329108569596 1.40000 0.8670147264905651 1.50000 0.9624236501192069 2.00000 1.316957896924817 3.00000 1.762747174039086 3.14159 1.811526272460853 4.00000 2.063437068895560 5.00000 2.292431669561178 10.0000 2.993222846126381 100.000 5.298292365610485 1000.00 7.600902209541989 ARCSIN_VALUES_TEST: ARCSIN_VALUES returns values of the arc sine X F(X) -0.100000 -0.1001674211615598 0.00000 0.000000000000000 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 1.119769514998634 1.00000 1.570796326794897 ARCSINH_VALUES_TEST: ARCSINH_VALUES returns values of the hyperbolic arc sine X F(X) -5.00000 -2.312438341272752 -1.00000 -0.8813735870195430 0.00000 0.000000000000000 0.100000 0.9983407889920756E-01 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 1.00000 0.8813735870195430 2.00000 1.443635475178810 3.00000 1.818446459232067 4.00000 2.094712547261101 5.00000 2.312438341272752 10.0000 2.998222950297970 100.000 5.298342365610589 1000.00 7.600902709541988 ARCTAN_VALUES_TEST: ARCTAN_VALUES returns values of the arc tangent X F(X) 0.00000 0.000000000000000 0.250000 0.2449786631268641 0.333333 0.3217505543966422 0.500000 0.4636476090008061 1.00000 0.7853981633974483 2.00000 1.107148717794090 3.00000 1.249045772398254 4.00000 1.325817663668033 5.00000 1.373400766945016 10.0000 1.471127674303735 20.0000 1.520837931072954 ARCTAN_INT_VALUES_TEST: ARCTAN_INT_VALUES returns values of the arctangent integral X F(X) 0.195312E-02 0.1953124172158848E-02 -0.390625E-02 -0.3906243377298071E-02 0.781250E-02 0.7812447019257650E-02 0.156250E-01 0.1562457618199653E-01 -0.312500E-01 -0.3124661034948540E-01 0.625000E-01 0.6247291133501440E-01 0.125000 0.1247841971738965 -0.250000 -0.2483017509823069 0.500000 0.4872223582945224 1.00000 0.9159655941772190 1.50000 1.274969448494380 -2.00000 -1.576015403446323 4.00000 2.425887841285909 8.00000 3.391163332629300 16.0000 4.417645091942219 -20.0000 -4.755671374954725 25.0000 5.096191215093411 30.0000 5.375917573571487 -50.0000 -6.164990478502749 100.000 7.243784301308353 ARCTAN2_VALUES_TEST: ARCTAN2_VALUES returns values of the arc tangent with two arguments. X Y ARCTAN2(X,Y) 0.00000 -1.00000 -1.570796326794897 0.500000 -0.866025 -1.047197551196598 0.866025 -0.500000 -0.5235987755982989 1.00000 0.00000 0.000000000000000 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.047197551196598 0.00000 1.00000 1.570796326794897 -0.500000 0.866025 2.094395102393196 -0.866025 0.500000 2.617993877991494 -1.00000 0.00000 3.141592653589793 -0.866025 -0.500000 -2.617993877991494 -0.500000 -0.866025 -2.094395102393196 0.00000 -1.00000 -1.570796326794897 0.500000 -0.866025 -1.047197551196598 0.866025 -0.500000 -0.5235987755982989 1.00000 0.00000 0.000000000000000 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.047197551196598 0.00000 1.00000 1.570796326794897 ARCTANH_VALUES_TEST: ARCTANH_VALUES returns values of the hyperbolic arc tangent X F(X) -0.500000 -0.5493061443340549 0.00000 0.000000000000000 0.100000E-02 0.1000000333333533E-02 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 1.098612288668110 0.900000 1.472219489583220 0.990000 2.646652412362246 0.999000 3.800201167250200 0.999999 7.254328619262047 BEI0_VALUES_TEST: BEI0_VALUES returns values of the Kelvin function BEI of order 0 X BEI0 0.00000 0.000000000000000 0.500000 0.6249321838219946E-01 1.00000 0.2495660400366597 1.50000 0.5575600623030867 2.00000 0.9722916273066612 2.50000 1.457182044159804 3.00000 1.937586785266043 3.50000 2.283249966853915 4.00000 2.292690322699300 4.50000 1.686017203632139 5.00000 0.1160343815502004 BEI1_VALUES_TEST: BEI1_VALUES returns values of the Kelvin function BEI of order 1 X BEI1 0.00000 0.000000000000000 0.500000 0.1711951797170153 1.00000 0.3075566313755366 1.50000 0.3678649890020899 2.00000 0.2997754370020335 2.50000 0.3866844396595048E-01 3.00000 -0.4874541770160708 3.50000 -1.344042373111174 4.00000 -2.563821688561078 4.50000 -4.105685408400878 5.00000 -5.797907901792625 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 returns values of the Kelvin function BER of order 0 X BEI0 0.00000 1.000000000000000 0.500000 0.9990234639908383 1.00000 0.9843817812130869 1.50000 0.9210721835462558 2.00000 0.7517341827138082 2.50000 0.3999684171295313 3.00000 -0.2213802495986939 3.50000 -1.193598179589928 4.00000 -2.563416557258580 4.50000 -4.299086551599756 5.00000 -6.230082478666358 BER1_VALUES_TEST: BER1_VALUES returns values of the Kelvin function BER of order 1 X BER1 0.00000 0.000000000000000 0.500000 -0.1822431237551121 1.00000 -0.3958682610197114 1.50000 -0.6648654179597691 2.00000 -0.9970776519264285 2.50000 -1.373096897645111 3.00000 -1.732644221128481 3.50000 -1.959644131289749 4.00000 -1.869248459031899 4.50000 -1.202821631480086 5.00000 0.3597766667766728 BERNOULLI_NUMBER_VALUES_TEST: BERNOULLI_NUMBER_VALUES returns values of the Bernoulli numbers. N BERNOULLI_NUMBER(N) 0 1.000000000000000 1 -0.5000000000000000 2 0.1666666666666667 3 0.000000000000000 4 -0.3333333333333333E-01 6 -0.2380952380952380E-01 8 -0.3333333333333333E-01 10 0.7575757575757575E-01 20 -529.1242424242424 30 601580873.9006424 BERNOULLI_POLY_VALUES_TEST: BERNOULLI_POLY_VALUES returns values of the Bernoulli polynomials. N X BERNOULLI_POLY(N,X) 0 0.200000 1.000000000000000 1 0.200000 -0.3000000000000000 2 0.200000 0.6666666666666667E-02 3 0.200000 0.4800000000000000E-01 4 0.200000 -0.7733333333333333E-02 5 0.200000 -0.2368000000000000E-01 6 0.200000 0.6913523809523810E-02 7 0.200000 0.2490880000000000E-01 8 0.200000 -0.1014997333333333E-01 9 0.200000 -0.4527820800000000E-01 10 0.200000 0.2332631815757576E-01 5 -0.500000 -0.3125000000000000 5 -0.400000 -0.1142400000000000 5 -0.300000 -0.1768000000000000E-01 5 -0.200000 0.1568000000000000E-01 5 -0.100000 0.1474000000000000E-01 5 0.00000 0.000000000000000 5 0.100000 -0.1524000000000000E-01 5 0.200000 -0.2368000000000000E-01 5 0.300000 -0.2282000000000000E-01 5 0.400000 -0.1376000000000000E-01 5 0.500000 0.000000000000000 5 0.600000 0.1376000000000000E-01 5 0.700000 0.2282000000000000E-01 5 0.800000 0.2368000000000000E-01 5 0.900000 0.1524000000000000E-01 5 1.00000 0.000000000000000 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 1.000000000000000 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 0.6250000000000000E-01 3 0 0.250000 0.4218750000000000 3 1 0.250000 0.4218750000000000 3 2 0.250000 0.1406250000000000 3 3 0.250000 0.1562500000000000E-01 4 0 0.250000 0.3164062500000000 4 1 0.250000 0.4218750000000000 4 2 0.250000 0.2109375000000000 4 3 0.250000 0.4687500000000000E-01 4 4 0.250000 0.3906250000000000E-02 BESSEL_I0_VALUES_TEST: BESSEL_I0_VALUES returns values of the Bessel I0 function. X I0(X) 0.00000 1.000000000000000 0.200000 1.010025027795146 0.400000 1.040401782229341 0.600000 1.092045364317340 0.800000 1.166514922869803 1.00000 1.266065877752008 1.20000 1.393725584134064 1.40000 1.553395099731217 1.60000 1.749980639738909 1.80000 1.989559356618051 2.00000 2.279585302336067 2.50000 3.289839144050123 3.00000 4.880792585865024 3.50000 7.378203432225480 4.00000 11.30192195213633 4.50000 17.48117185560928 5.00000 27.23987182360445 6.00000 67.23440697647798 8.00000 427.5641157218048 10.0000 2815.716628466254 BESSEL_I0_INT_VALUES_TEST: BESSEL_I0_INT_VALUES returns values of the integral of the Bessel I0 function. X I0_INT(X) 0.195312E-02 0.1953125620881805E-02 -0.390625E-02 -0.3906254967056573E-02 0.625000E-01 0.6252034803254657E-01 0.125000 0.1251628558136697 -0.500000 -0.5105148087974031 1.00000 1.086521097023590 2.00000 2.775001905428253 -4.00000 -13.77520886803972 8.00000 464.2437205810611 18.0000 6411186.765802158 -18.5000 -10414860.80317586 20.0000 44758598.91385575 -21.0000 -118529853.1155829 22.0000 314300782.2071599 -23.0000 -834402129.0079432 24.0000 2217536757.907430 25.0000 5899173184.280364 -27.0000 -41857073244.69152 30.0000 795538858184.7236 40.0000 0.1508971508271920E+17 BESSEL_I0_SPHERICAL_VALUES_TEST: BESSEL_I0_SPHERICAL_VALUES returns values of the spherical Bessel i0 function. X i0(X) 0.100000 1.001667500198440 0.200000 1.006680012705470 0.400000 1.026880814507039 0.600000 1.061089303580402 0.800000 1.110132477734529 1.00000 1.175201193643801 1.20000 1.257884462843477 1.40000 1.360215358179667 1.60000 1.484729970750144 1.80000 1.634541271164267 2.00000 1.813430203923509 2.20000 2.025956895698133 2.40000 2.277595505698373 2.60000 2.574897010920645 2.80000 2.925685126512827 3.00000 3.339291642469967 3.20000 3.826838748926716 3.40000 4.401577467270101 3.60000 5.079293155726485 3.80000 5.878791279137455 4.00000 6.822479299281938 BESSEL_I1_VALUES_TEST: BESSEL_I1_VALUES returns values of the Bessel I1 function. X I1(X) 0.00000 0.000000000000000 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.00000 0.5651591039924850 1.20000 0.7146779415526431 1.40000 0.8860919814143274 1.60000 1.084810635129880 1.80000 1.317167230391899 2.00000 1.590636854637329 2.50000 2.516716245288698 3.00000 3.953370217402609 3.50000 6.205834922258365 4.00000 9.759465153704451 4.50000 15.38922275373592 5.00000 24.33564214245053 6.00000 61.34193677764024 8.00000 399.8731367825601 10.0000 2670.988303701255 BESSEL_I1_SPHERICAL_VALUES_TEST: BESSEL_I1_SPHERICAL_VALUES returns values of the spherical Bessel i1 function. X i1(X) 0.100000 0.3336667857363341E-01 0.200000 0.6693371456802955E-01 0.400000 0.1354788933285401 0.600000 0.2072931911031093 0.800000 0.2841280857128948 1.00000 0.3678794411714423 1.20000 0.4606425870674146 1.40000 0.5647736480096238 1.60000 0.6829590627779635 1.80000 0.8182955028627777 2.00000 0.9743827435800611 2.20000 1.155432469636406 2.40000 1.366396525527973 2.60000 1.613118767572064 2.80000 1.902515460838681 3.00000 2.242790117769266 3.20000 2.643689828630357 3.40000 3.116811526884873 3.60000 3.675968313148932 3.80000 4.337627987747642 4.00000 5.121438384183637 BESSEL_IN_VALUES_TEST: BESSEL_IN_VALUES returns values of the Bessel In function. N X I(N,X) 2 0.200000 0.5016687513894678E-02 2 1.00000 0.1357476697670383 2 2.00000 0.6889484476987382 2 2.50000 1.276466147819164 2 3.00000 2.245212440929951 2 5.00000 17.50561496662424 2 10.0000 2281.518967726004 2 20.0000 39312785.22104076 3 1.00000 0.2216842492433190E-01 3 2.00000 0.2127399592398527 3 5.00000 10.33115016915114 3 10.0000 1758.380716610853 3 50.0000 0.2677764138883941E+21 5 1.00000 0.2714631559569719E-03 5 2.00000 0.9825679323131702E-02 5 5.00000 2.157974547322546 5 10.0000 777.1882864032600 5 50.0000 0.2278548307911282E+21 10 1.00000 0.2752948039836874E-09 10 2.00000 0.3016963879350684E-06 10 5.00000 0.4580044419176051E-02 10 10.0000 21.89170616372337 10 50.0000 0.1071597159477637E+21 20 1.00000 0.3966835985819020E-24 20 2.00000 0.4310560576109548E-18 20 5.00000 0.5024239357971806E-10 20 10.0000 0.1250799735644948E-03 20 50.0000 0.5442008402752998E+19 BESSEL_IX_VALUES_TEST: BESSEL_IX_VALUES returns values of the Bessel In function with REAL argument N. N X I(N,X) 0.500000 0.200000 0.3592084175833614 0.500000 1.00000 0.9376748882454876 0.500000 2.00000 2.046236863089055 0.500000 2.50000 3.053093538196718 0.500000 3.00000 4.614822903407601 0.500000 5.00000 26.47754749755907 0.500000 10.0000 2778.784603874571 0.500000 20.0000 43279746.27242893 1.50000 1.00000 0.2935253263474798 1.50000 2.00000 1.099473188633110 1.50000 5.00000 21.18444226479414 1.50000 10.0000 2500.906154942118 1.50000 50.0000 0.2866653715931464E+21 2.50000 1.00000 0.5709890920304825E-01 2.50000 2.00000 0.3970270801393905 2.50000 5.00000 13.76688213868258 2.50000 10.0000 2028.512757391936 2.50000 50.0000 0.2753157630035402E+21 1.25000 1.00000 0.4139416015642352 1.25000 2.00000 1.340196758982897 1.25000 5.00000 22.85715510364670 1.25000 10.0000 2593.006763432002 1.25000 50.0000 0.2886630075077766E+21 2.75000 1.00000 0.3590910483251082E-01 2.75000 2.00000 0.2931108636266483 2.75000 5.00000 11.99397010023068 2.75000 10.0000 1894.575731562383 2.75000 50.0000 0.2716911375760483E+21 BESSEL_J_SPHERICAL_VALUES_TEST: BESSEL_J_SPHERICAL_VALUES returns values of the spherical Bessel j function. N X jn(X) 0 0.905000 0.8689780717709105 1 0.905000 0.2776712616989048 2 0.905000 0.5147914933043151E-01 3 0.905000 0.6743927971987495E-02 4 0.905000 0.6838294584220406E-03 5 0.905000 0.5658597917091951E-04 6 0.905000 0.3955923765931341E-05 7 0.905000 0.2394450910776484E-06 8 0.905000 0.1277940110150618E-07 9 0.905000 0.6099572379372921E-09 10 0.905000 0.2633096568558721E-10 0 10.0000 -0.5440211108893698E-01 1 10.0000 0.7846694179875155E-01 2 10.0000 0.7794219362856245E-01 3 10.0000 -0.3949584498447032E-01 4 10.0000 -0.1055892851176917 5 10.0000 -0.5553451162145218E-01 6 10.0000 0.4450132233409427E-01 7 10.0000 0.1133862306557747 8 10.0000 0.1255780236495678 9 10.0000 0.1000964095484906 10 10.0000 0.6460515449256427E-01 BESSEL_J0_VALUES_TEST: BESSEL_J0_VALUES returns values of the Bessel J0 function. X J0(X) -5.00000 -0.1775967713143383 -4.00000 -0.3971498098638474 -3.00000 -0.2600519549019334 -2.00000 0.2238907791412357 -1.00000 0.7651976865579666 0.00000 1.000000000000000 1.00000 0.7651976865579666 2.00000 0.2238907791412357 3.00000 -0.2600519549019334 4.00000 -0.3971498098638474 5.00000 -0.1775967713143383 6.00000 0.1506452572509969 7.00000 0.3000792705195556 8.00000 0.1716508071375539 9.00000 -0.9033361118287613E-01 10.0000 -0.2459357644513483 11.0000 -0.1711903004071961 12.0000 0.4768931079683354E-01 13.0000 0.2069261023770678 14.0000 0.1710734761104587 15.0000 -0.1422447282678077E-01 BESSEL_J0_INT_VALUES_TEST: BESSEL_J0_INT_VALUES returns values of the integral of the Bessel J0 function. X J0_INT(X) 0.976562E-03 0.9765624223897882E-03 0.390625E-02 0.3906245032949111E-02 -0.625000E-01 -0.6247965792791793E-01 0.125000 0.1248373349212048 -0.500000 -0.4896805066460451 1.00000 0.9197304100897602 -2.00000 -1.425770293197027 4.00000 1.024734159460607 -8.00000 -1.210746834830450 16.0000 1.100865203273619 -16.5000 -1.006033482990413 18.0000 0.8133057266248596 -20.0000 -1.058378821421128 25.0000 0.8710149211654588 -30.0000 -0.8842490888254749 40.0000 1.125776150359991 -50.0000 -0.9014121225818346 75.0000 0.9144134436964779 -80.0000 -0.9448228193833440 100.000 0.9226625569601661 BESSEL_J0_SPHERICAL_VALUES_TEST: BESSEL_J0_SPHERICAL_VALUES returns values of the spherical Bessel j0 function. X j0(X) 0.100000 0.9983341664682815 0.200000 0.9933466539753061 0.400000 0.9735458557716262 0.600000 0.9410707889917256 0.800000 0.8966951136244035 1.00000 0.8414709848078965 1.20000 0.7766992383060221 1.40000 0.7038926642774715 1.60000 0.6247335019009407 1.80000 0.5410264615989973 2.00000 0.4546487134128408 2.20000 0.3674983653725410 2.40000 0.2814429918963129 2.60000 0.1982697583928709 2.80000 0.1196386250556803 3.00000 0.4704000268662241E-01 3.20000 -0.1824191982111872E-01 3.40000 -0.7515914765495040E-01 3.60000 -0.1229223453596812 3.80000 -0.1610152344586103 4.00000 -0.1892006238269821 BESSEL_J0_ZERO_VALUES_TEST: BESSEL_J0_ZERO_VALUES returns 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 24.35247153074930 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 52.62405184111500 18 55.76551075501998 19 58.90698392608094 20 62.04846919022717 21 65.18996480020687 22 68.33146932985680 23 71.47298160359374 24 74.61450064370183 25 77.75602563038805 26 80.89755587113763 27 84.03909077693820 28 87.18062984364116 29 90.32217263721049 30 93.46371878194478 BESSEL_J1_VALUES_TEST: BESSEL_J1_VALUES returns values of the Bessel J1 function. X J1(X) -5.00000 0.3275791375914652 -4.00000 0.6604332802354913E-01 -3.00000 -0.3390589585259365 -2.00000 -0.5767248077568734 -1.00000 -0.4400505857449335 0.00000 0.000000000000000 1.00000 0.4400505857449335 2.00000 0.5767248077568734 3.00000 0.3390589585259365 4.00000 -0.6604332802354913E-01 5.00000 -0.3275791375914652 6.00000 -0.2766838581275656 7.00000 -0.4682823482345833E-02 8.00000 0.2346363468539146 9.00000 0.2453117865733253 10.0000 0.4347274616886144E-01 11.0000 -0.1767852989567215 12.0000 -0.2234471044906276 13.0000 -0.7031805212177837E-01 14.0000 0.1333751546987933 15.0000 0.2051040386135228 BESSEL_J1_SPHERICAL_VALUES_TEST: BESSEL_J1_SPHERICAL_VALUES returns values of the spherical Bessel j1 function. X j1(X) 0.100000 0.3330001190255757E-01 0.200000 0.6640038067032222E-01 0.400000 0.1312121544218529 0.600000 0.1928919568034122 0.800000 0.2499855053465475 1.00000 0.3011686789397568 1.20000 0.3452845698577903 1.40000 0.3813753724123076 1.60000 0.4087081401263934 1.80000 0.4267936423844913 2.00000 0.4353977749799916 2.20000 0.4345452193763121 2.40000 0.4245152947656493 2.60000 0.4058301968314685 2.80000 0.3792360591872637 3.00000 0.3456774997623560 3.20000 0.3062665174917607 3.40000 0.2622467779189737 3.60000 0.2149544641595738 3.80000 0.1657769677515280 4.00000 0.1161107492591575 BESSEL_JN_VALUES_TEST: BESSEL_JN_VALUES returns values of the Bessel Jn function. N X J(N,X) 2 1.00000 0.1149034849319005 2 2.00000 0.3528340286156377 2 5.00000 0.4656511627775222E-01 2 10.0000 0.2546303136851206 2 50.0000 -0.5971280079425882E-01 5 1.00000 0.2497577302112344E-03 5 2.00000 0.7039629755871685E-02 5 5.00000 0.2611405461201701 5 10.0000 -0.2340615281867936 5 50.0000 -0.8140024769656964E-01 10 1.00000 0.2630615123687453E-09 10 2.00000 0.2515386282716737E-06 10 5.00000 0.1467802647310474E-02 10 10.0000 0.2074861066333589 10 50.0000 -0.1138478491494694 20 1.00000 0.3873503008524658E-24 20 2.00000 0.3918972805090754E-18 20 5.00000 0.2770330052128942E-10 20 10.0000 0.1151336924781340E-04 20 50.0000 -0.1167043527595797 BESSEL_JX_VALUES_TEST: BESSEL_JX_VALUES returns values of the Bessel Jn function with REAL argument N. N X J(N,X) 0.500000 0.200000 0.3544507442114011 0.500000 1.00000 0.6713967071418031 0.500000 2.00000 0.5130161365618278 0.500000 2.50000 0.3020049060623657 0.500000 3.00000 0.6500818287737578E-01 0.500000 5.00000 -0.3421679847981618 0.500000 10.0000 -0.1372637357550505 0.500000 20.0000 0.1628807638550299 1.50000 1.00000 0.2402978391234270 1.50000 2.00000 0.4912937786871623 1.50000 5.00000 -0.1696513061447408 1.50000 10.0000 0.1979824927558931 1.50000 50.0000 -0.1094768729883180 2.50000 1.00000 0.4949681022847794E-01 2.50000 2.00000 0.2239245314689158 2.50000 5.00000 0.2403772011113174 2.50000 10.0000 0.1966584835818184 2.50000 50.0000 0.2303721950962553E-01 1.25000 1.00000 0.3314145508558904 1.25000 2.00000 0.5461734240402840 1.25000 5.00000 -0.2616584152094124 1.25000 10.0000 0.1296035513791289 1.25000 50.0000 -0.1117432171933552 2.75000 1.00000 0.3142623570527935E-01 2.75000 2.00000 0.1717922192746527 2.75000 5.00000 0.3126634069544786 2.75000 10.0000 0.1340289119304364 2.75000 50.0000 0.6235967135106445E-01 BESSEL_K0_VALUES_TEST: BESSEL_K0_VALUES returns values of the Bessel K0 function. X K0(X) 0.100000 2.427069024702017 0.200000 1.752703855528146 0.400000 1.114529134524434 0.600000 0.7775220919047293 0.800000 0.5653471052658957 1.00000 0.4210244382407083 1.20000 0.3185082202865936 1.40000 0.2436550611815419 1.60000 0.1879547519693323 1.80000 0.1459314004898280 2.00000 0.1138938727495334 2.50000 0.6234755320036619E-01 3.00000 0.3473950438627925E-01 3.50000 0.1959889717036849E-01 4.00000 0.1115967608585302E-01 4.50000 0.6399857243233975E-02 5.00000 0.3691098334042594E-02 6.00000 0.1243994328013123E-02 8.00000 0.1464707052228154E-03 10.0000 0.1778006231616765E-04 BESSEL_K0_INT_VALUES_TEST: BESSEL_K0_INT_VALUES returns values of the integral of the Bessel K0 function. X K0_INT(X) 0.976562E-03 0.7858792956346679E-02 0.390625E-02 0.2601999161733058E-01 0.625000E-01 0.2431184223754117 0.125000 0.3999963375048051 0.500000 0.9271025209311491 1.00000 1.242509848623778 2.00000 1.473675734316829 4.00000 1.560649570605174 5.00000 1.567387390728366 6.00000 1.569634553269374 6.50000 1.570115344325079 8.00000 1.570657485289444 10.0000 1.570779311615979 12.0000 1.570794206646577 15.0000 1.570796231546919 20.0000 1.570796326234015 30.0000 1.570796326794876 50.0000 1.570796326794897 80.0000 1.570796326794897 100.000 1.570796326794897 BESSEL_K1_VALUES_TEST: BESSEL_K1_VALUES returns values of the Bessel K1 function. X K1(X) 0.100000 9.853844780870606 0.200000 4.775972543220472 0.400000 2.184354424732687 0.600000 1.302834939763502 0.800000 0.8617816344721803 1.00000 0.6019072301972346 1.20000 0.4345923910607150 1.40000 0.3208359022298758 1.60000 0.2406339113576119 1.80000 0.1826230998017470 2.00000 0.1398658818165224 2.50000 0.7389081634774707E-01 3.00000 0.4015643112819418E-01 3.50000 0.2223939292592383E-01 4.00000 0.1248349888726843E-01 4.50000 0.7078094908968090E-02 5.00000 0.4044613445452164E-02 6.00000 0.1343919717735509E-02 8.00000 0.1553692118050011E-03 10.0000 0.1864877345382558E-04 BESSEL_KN_VALUES_TEST: BESSEL_KN_VALUES returns values of the Bessel Kn function. N X K(N,X) 2 0.200000 49.51242928773287 2 1.00000 1.624838898635177 2 2.00000 0.2537597545660559 2 2.50000 0.1214602062785638 2 3.00000 0.6151045847174204E-01 2 5.00000 0.5308943712223460E-02 2 10.0000 0.2150981700693277E-04 2 20.0000 0.6329543612292228E-09 3 1.00000 7.101262824737945 3 2.00000 0.6473853909486342 3 5.00000 0.8291768415230933E-02 3 10.0000 0.2725270025659869E-04 3 50.0000 0.3727936773826211E-22 5 1.00000 360.9605896012407 5 2.00000 9.431049100596468 5 5.00000 0.3270627371203186E-01 5 10.0000 0.5754184998531228E-04 5 50.0000 0.4367182254100986E-22 10 1.00000 180713289.9010295 10 2.00000 162482.4039795591 10 5.00000 9.758562829177810 10 10.0000 0.1614255300390670E-02 10 50.0000 0.9150988209987996E-22 20 1.00000 0.6294369360424535E+23 20 2.00000 0.5770856852700241E+17 20 5.00000 482700052.0621485 20 10.0000 178.7442782077055 20 50.0000 0.1706148379722035E-20 BESSEL_KX_VALUES_TEST: BESSEL_KX_VALUES returns values of the Bessel Kn function with REAL argument N. N X K(N,X) 0.500000 0.200000 2.294489339798475 0.500000 1.00000 0.4610685044478946 0.500000 2.00000 0.1199377719680614 0.500000 2.50000 0.6506594315400999E-01 0.500000 3.00000 0.3602598513176459E-01 0.500000 5.00000 0.3776613374642883E-02 0.500000 10.0000 0.1799347809370518E-04 0.500000 20.0000 0.5776373974707445E-09 1.50000 1.00000 0.9221370088957891 1.50000 2.00000 0.1799066579520922 1.50000 5.00000 0.4531936049571459E-02 1.50000 10.0000 0.1979282590307570E-04 1.50000 50.0000 0.3486992497366216E-22 2.50000 1.00000 3.227479531135262 2.50000 2.00000 0.3897977588961997 2.50000 5.00000 0.6495775004385758E-02 2.50000 10.0000 0.2393132586462789E-04 2.50000 50.0000 0.3627839645299048E-22 1.25000 1.00000 0.7311451879202114 1.25000 2.00000 0.1567475478393932 1.25000 5.00000 0.4257389528177461E-02 1.25000 10.0000 0.1915541065869563E-04 1.25000 50.0000 0.3463337593569306E-22 2.75000 1.00000 4.731184839919541 2.75000 2.00000 0.4976876225514758 2.75000 5.00000 0.7300864610941163E-02 2.75000 10.0000 0.2546421294106458E-04 2.75000 50.0000 0.3675275677913656E-22 BESSEL_Y0_VALUES_TEST: BESSEL_Y0_VALUES returns values of the Bessel Y0 function. X Y0(X) 0.100000 -1.534238651350367 1.00000 0.8825696421567696E-01 2.00000 0.5103756726497451 3.00000 0.3768500100127904 4.00000 -0.1694073932506499E-01 5.00000 -0.3085176252490338 6.00000 -0.2881946839815792 7.00000 -0.2594974396720926E-01 8.00000 0.2235214893875662 9.00000 0.2499366982850247 10.0000 0.5567116728359939E-01 11.0000 -0.1688473238920795 12.0000 -0.2252373126343614 13.0000 -0.7820786452787591E-01 14.0000 0.1271925685821837 15.0000 0.2054642960389183 BESSEL_Y0_INT_VALUES_TEST: BESSEL_Y0_INT_VALUES returns values of the integral of the Bessel Y0 function. X Y0_INT(X) 0.195312E-02 -0.9144264286017211E-02 0.781250E-02 -0.2968204739039759E-01 0.125000 -0.2539143127658539 0.500000 -0.5617954559146403 1.00000 -0.6370693766074231 2.00000 -0.2821928500851009 4.00000 0.3836696478531256 6.00000 -0.1259506128579893 10.0000 0.2412903183226668 16.0000 0.1713806975762704 16.2500 0.1895814262713408 17.0000 0.1720384613644971 20.0000 -0.1682159767721503 25.0000 -0.9360792735142899E-01 30.0000 0.8822971194803665E-01 40.0000 -0.8932466273627416E-02 50.0000 -0.5481407100006349E-01 70.0000 -0.9495824600346638E-01 100.000 -0.1959806485340497E-01 125.000 -0.8308477235715477E-02 BESSEL_Y0_SPHERICAL_VALUES_TEST: BESSEL_Y0_SPHERICAL_VALUES returns values of the spherical Bessel Y0 function. X y0(X) 0.100000 -9.950041652780259 0.200000 -4.900332889206208 0.400000 -2.302652485007213 0.600000 -1.375559358182797 0.800000 -0.8708833866839568 1.00000 -0.5403023058681397 1.20000 -0.3019647953972280 1.40000 -0.1214051020716007 1.60000 0.1824970143830545E-01 1.80000 0.1262233859406039 2.00000 0.2080734182735712 2.20000 0.2675005078433390 2.40000 0.3072473814755190 2.60000 0.3295725974495951 2.80000 0.3365079788102351 3.00000 0.3299974988668152 3.20000 0.3119671174358603 3.40000 0.2843524095821944 3.60000 0.2490995600928186 3.80000 0.2081493978722149 4.00000 0.1634109052159030 BESSEL_Y1_VALUES_TEST: BESSEL_Y1_VALUES returns values of the Bessel Y1 function. X Y1(X) 0.100000 -6.458951094702027 1.00000 -0.7812128213002887 2.00000 -0.1070324315409375 3.00000 0.3246744247918000 4.00000 0.3979257105571000 5.00000 0.1478631433912268 6.00000 -0.1750103443003983 7.00000 -0.3026672370241849 8.00000 -0.1580604617312475 9.00000 0.1043145751967159 10.0000 0.2490154242069539 11.0000 0.1637055374149429 12.0000 -0.5709921826089652E-01 13.0000 -0.2100814084206935 14.0000 -0.1666448418561723 15.0000 0.2107362803687351E-01 BESSEL_Y1_SPHERICAL_VALUES_TEST: BESSEL_Y1_SPHERICAL_VALUES returns values of the spherical Bessel Y1 function. X y1(X) 0.100000 -100.4987506942709 0.200000 -25.49501110000635 0.400000 -6.730177068289658 0.600000 -3.233669719296388 0.800000 -1.985299346979349 1.00000 -1.381773290676036 1.20000 -1.028336567803712 1.40000 -0.7906105943286149 1.60000 -0.6133274385019998 1.80000 -0.4709023582986618 2.00000 -0.3506120042760553 2.20000 -0.2459072254437506 2.40000 -0.1534232496148467 2.60000 -0.7151106706610352E-01 2.80000 0.5427959479750482E-03 3.00000 0.6295916360231597E-01 3.20000 0.1157316440198251 3.40000 0.1587922092967723 3.60000 0.1921166676076864 3.80000 0.2157913917934037 4.00000 0.2300533501309578 BESSEL_YN_VALUES_TEST: BESSEL_YN_VALUES returns values of the Bessel Yn function. N X Y(N,X) 2 1.00000 -1.650682606816254 2 2.00000 -0.6174081041906827 2 5.00000 0.3676628826055245 2 10.0000 -0.5868082442208615E-02 2 50.0000 0.9579316872759649E-01 5 1.00000 -260.4058666258122 5 2.00000 -9.935989128481975 5 5.00000 -0.4536948224911019 5 10.0000 0.1354030476893623 5 50.0000 -0.7854841391308165E-01 10 1.00000 -121618014.2786892 10 2.00000 -129184.5422080393 10 5.00000 -25.12911009561010 10 10.0000 -0.3598141521834027 10 50.0000 0.5723897182053514E-02 20 1.00000 -0.4113970314835505E+23 20 2.00000 -0.4081651388998367E+17 20 5.00000 -593396529.6914321 20 10.0000 -1597.483848269626 20 50.0000 0.1644263394811578E-01 BESSEL_YX_VALUES_TEST: BESSEL_YX_VALUES returns values of the Bessel Yn function with REAL argument N. N X Y(N,X) 0.500000 0.200000 -1.748560416961876 0.500000 1.00000 -0.4310988680183761 0.500000 2.00000 0.2347857104062485 0.500000 2.50000 0.4042783022390569 0.500000 3.00000 0.4560488207946332 0.500000 5.00000 -0.1012177091851084 0.500000 10.0000 0.2117088663313982 0.500000 20.0000 -0.7280690478506185E-01 1.50000 1.00000 -1.102495575160179 1.50000 2.00000 -0.3956232813587035 1.50000 5.00000 0.3219244429611401 1.50000 10.0000 0.1584346223881903 1.50000 50.0000 0.2742813676191382E-01 2.50000 1.00000 -2.876387857462161 2.50000 2.00000 -0.8282206324443037 2.50000 5.00000 0.2943723749617925 2.50000 10.0000 -0.1641784796149411 2.50000 50.0000 0.1105304445562544 1.25000 1.00000 -0.9319659251969881 1.25000 2.00000 -0.2609445010948933 1.25000 5.00000 0.2492796362185881 1.25000 10.0000 0.2174410301416733 1.25000 50.0000 -0.1578576650557229E-01 2.75000 1.00000 -4.023453301501028 2.75000 2.00000 -0.9588998694752389 2.75000 5.00000 0.2264260361047367 2.75000 10.0000 -0.2193617736566760 2.75000 50.0000 0.9413988344515077E-01 BETA_VALUES_TEST: BETA_VALUES returns values of the Beta function. X Y BETA(X,Y) 0.200000 1.00000 5.000000000000000 0.400000 1.00000 2.500000000000000 0.600000 1.00000 1.666666666666667 0.800000 1.00000 1.250000000000000 1.00000 0.200000 5.000000000000000 1.00000 0.400000 2.500000000000000 1.00000 1.00000 1.000000000000000 2.00000 2.00000 0.1666666666666667 3.00000 3.00000 0.3333333333333333E-01 4.00000 4.00000 0.7142857142857143E-02 5.00000 5.00000 0.1587301587301587E-02 6.00000 2.00000 0.2380952380952381E-01 6.00000 3.00000 0.5952380952380952E-02 6.00000 4.00000 0.1984126984126984E-02 6.00000 5.00000 0.7936507936507937E-03 6.00000 6.00000 0.3607503607503608E-03 7.00000 7.00000 0.8325008325008325E-04 BETA_CDF_VALUES_TEST: BETA_CDF_VALUES returns values of the Beta CDF. A B X CDF 0.500000 0.500000 0.100000E-01 0.637686E-01 0.500000 0.500000 0.100000 0.204833 0.500000 0.500000 1.00000 1.00000 1.00000 0.500000 0.00000 0.00000 1.00000 0.500000 0.100000E-01 0.501256E-02 1.00000 0.500000 0.100000 0.513167E-01 1.00000 0.500000 0.500000 0.292893 1.00000 1.00000 0.500000 0.500000 2.00000 2.00000 0.100000 0.280000E-01 2.00000 2.00000 0.200000 0.104000 2.00000 2.00000 0.300000 0.216000 2.00000 2.00000 0.400000 0.352000 2.00000 2.00000 0.500000 0.500000 2.00000 2.00000 0.600000 0.648000 2.00000 2.00000 0.700000 0.784000 2.00000 2.00000 0.800000 0.896000 2.00000 2.00000 0.900000 0.972000 5.50000 5.00000 0.500000 0.436191 10.0000 0.500000 0.900000 0.151641 10.0000 5.00000 0.500000 0.897827E-01 10.0000 5.00000 1.00000 1.00000 10.0000 10.0000 0.500000 0.500000 20.0000 5.00000 0.800000 0.459877 20.0000 10.0000 0.600000 0.214682 20.0000 10.0000 0.800000 0.950736 20.0000 20.0000 0.500000 0.500000 20.0000 20.0000 0.600000 0.897941 30.0000 10.0000 0.700000 0.224130 30.0000 10.0000 0.800000 0.758641 40.0000 20.0000 0.700000 0.700178 1.00000 0.500000 0.100000 0.513167E-01 1.00000 0.500000 0.200000 0.105573 1.00000 0.500000 0.300000 0.163340 1.00000 0.500000 0.400000 0.225403 1.00000 2.00000 0.200000 0.360000 1.00000 3.00000 0.200000 0.488000 1.00000 4.00000 0.200000 0.590400 1.00000 5.00000 0.200000 0.672320 2.00000 2.00000 0.300000 0.216000 3.00000 2.00000 0.300000 0.837000E-01 4.00000 2.00000 0.300000 0.307800E-01 5.00000 2.00000 0.300000 0.109350E-01 1.30625 11.7562 0.225609 0.918885 1.30625 11.7562 0.335568E-01 0.210530 1.30625 11.7562 0.295222E-01 0.182413 BETA_INC_VALUES_TEST: BETA_INC_VALUES returns values of the incomplete Beta function. A B X BETA_INC(A,B)(X) 0.500000 0.500000 0.100000E-01 0.637686E-01 0.500000 0.500000 0.100000 0.204833 0.500000 0.500000 1.00000 1.00000 1.00000 0.500000 0.00000 0.00000 1.00000 0.500000 0.100000E-01 0.501256E-02 1.00000 0.500000 0.100000 0.513167E-01 1.00000 0.500000 0.500000 0.292893 1.00000 1.00000 0.500000 0.500000 2.00000 2.00000 0.100000 0.280000E-01 2.00000 2.00000 0.200000 0.104000 2.00000 2.00000 0.300000 0.216000 2.00000 2.00000 0.400000 0.352000 2.00000 2.00000 0.500000 0.500000 2.00000 2.00000 0.600000 0.648000 2.00000 2.00000 0.700000 0.784000 2.00000 2.00000 0.800000 0.896000 2.00000 2.00000 0.900000 0.972000 5.50000 5.00000 0.500000 0.436191 10.0000 0.500000 0.900000 0.151641 10.0000 5.00000 0.500000 0.897827E-01 10.0000 5.00000 1.00000 1.00000 10.0000 10.0000 0.500000 0.500000 20.0000 5.00000 0.800000 0.459877 20.0000 10.0000 0.600000 0.214682 20.0000 10.0000 0.800000 0.950736 20.0000 20.0000 0.500000 0.500000 20.0000 20.0000 0.600000 0.897941 30.0000 10.0000 0.700000 0.224130 30.0000 10.0000 0.800000 0.758641 40.0000 20.0000 0.700000 0.700178 1.00000 0.500000 0.100000 0.513167E-01 1.00000 0.500000 0.200000 0.105573 1.00000 0.500000 0.300000 0.163340 1.00000 0.500000 0.400000 0.225403 1.00000 2.00000 0.200000 0.360000 1.00000 3.00000 0.200000 0.488000 1.00000 4.00000 0.200000 0.590400 1.00000 5.00000 0.200000 0.672320 2.00000 2.00000 0.300000 0.216000 3.00000 2.00000 0.300000 0.837000E-01 4.00000 2.00000 0.300000 0.307800E-01 5.00000 2.00000 0.300000 0.109350E-01 1.30625 11.7562 0.225609 0.918885 1.30625 11.7562 0.335568E-01 0.210530 1.30625 11.7562 0.295222E-01 0.182413 BETA_LOG_VALUES_TEST: BETA_LOG_VALUES returns values of the logarithm of the Beta function. X Y BETA_LOG(X,Y) 0.200000 1.00000 1.609437912434100 0.400000 1.00000 0.9162907318741551 0.600000 1.00000 0.5108256237659907 0.800000 1.00000 0.2231435513142098 1.00000 0.200000 1.609437912434100 1.00000 0.400000 0.9162907318741551 1.00000 1.00000 0.000000000000000 2.00000 2.00000 -1.791759469228055 3.00000 3.00000 -3.401197381662155 4.00000 4.00000 -4.941642422609304 5.00000 5.00000 -6.445719819385578 6.00000 2.00000 -3.737669618283368 6.00000 3.00000 -5.123963979403259 6.00000 4.00000 -6.222576268071369 6.00000 5.00000 -7.138866999945524 6.00000 6.00000 -7.927324360309794 7.00000 7.00000 -9.393661429103220 BETA_NONCENTRAL_CDF_VALUES_TEST: BETA_NONCENTRAL_CDF_VALUES returns values of the Beta CDF. A B LAMBDA X CDF 5.00 5.00 54.00 0.864000 0.4563021000000000 5.00 5.00 140.00 0.900000 0.1041337000000000 5.00 5.00 170.00 0.956000 0.6022353000000000 10.00 10.00 54.00 0.868600 0.9187770000000000 10.00 10.00 140.00 0.900000 0.6008106000000000 10.00 10.00 250.00 0.900000 0.9028500000000000E-01 20.00 20.00 54.00 0.878700 0.9998655000000000 20.00 20.00 140.00 0.900000 0.9925997000000000 20.00 20.00 250.00 0.922000 0.9641111999999999 10.00 20.00 150.00 0.868000 0.9376626573000000 10.00 10.00 120.00 0.900000 0.7306817858000000 15.00 5.00 80.00 0.880000 0.1604256918000000 20.00 10.00 110.00 0.850000 0.1867485313000000 20.00 30.00 65.00 0.660000 0.6559386874000001 20.00 50.00 130.00 0.720000 0.9796881486000000 30.00 20.00 80.00 0.720000 0.1162386423000000 30.00 40.00 130.00 0.800000 0.9930430054000000 10.00 5.00 20.00 0.644000 0.5068992730000000E-01 10.00 10.00 54.00 0.700000 0.1030959706000000 10.00 30.00 80.00 0.780000 0.9978417832000001 15.00 20.00 120.00 0.760000 0.2555552369000000 10.00 5.00 55.00 0.795000 0.6683070640000000E-01 12.00 17.00 64.00 0.560000 0.1136010670000000E-01 30.00 30.00 140.00 0.800000 0.7813366615000000 35.00 30.00 20.00 0.670000 0.8867126477000000 BETA_PDF_VALUES_TEST: BETA_PDF_VALUES returns values of the Beta PDF. ALPHA BETA X PDF 1.09209 4.78159 0.866722 0.282614E-02 2.80848 2.07654 0.460776E-01 0.420895E-01 1.28789 0.549784 0.221162E-01 0.218406 3.16983 0.308636 0.458254 0.133514 2.00653 3.77337 0.832083 0.107057 0.919186E-02 4.48752 0.352059 0.579639E-02 0.472724 0.680845E-01 0.898529 0.551880 4.20424 0.615520 -0.169242E-01 0.00000 1.30151 4.56242 0.971888E-01 2.87907 1.75814 4.11444 0.262167 2.12699 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 2 0.5000E-01 0 0.9025000000000000 2 0.5000E-01 1 0.9975000000000001 2 0.5000E-01 2 1.000000000000000 2 0.5000 0 0.2500000000000000 2 0.5000 1 0.7500000000000000 4 0.2500 0 0.3164062500000000 4 0.2500 1 0.7382812500000000 4 0.2500 2 0.9492187500000000 4 0.2500 3 0.9960937500000000 10 0.5000E-01 4 0.9999363101685547 10 0.1000 4 0.9983650626000000 10 0.1500 4 0.9901259090013672 10 0.2000 4 0.9672065023999999 10 0.2500 4 0.9218730926513672 10 0.3000 4 0.8497316673999999 10 0.4000 4 0.6331032576000000 10 0.5000 4 0.3769531250000000 BINOMIAL_PDF_VALUES_TEST: BINOMIAL_PDF_VALUES returns values of the Binomial Probability Density Function. A B X CDF 5 0.8295092339327006 5 0.3927408939646697 12 0.6611873491603133E-01 5 0.6199968732461383E-03 6 0.4382899777910710E-01 0 0.7642112247331240 13 0.4495389603071763 0 0.4260353334364943E-03 9 0.7972869541062562 7 0.3029482891457940 1 0.3507523379805466 1 0.3507523379805466 2 0.8590968552798568 0 0.1985369619202562E-01 17 0.7512364073964213E-02 2 0.6854388879646552E-02 6 0.1136640464424993 6 0.2156446446382985E-05 8 0.2671322702601793 7 0.5691150511772053E-03 BIVARIATE_NORMAL_CDF_VALUES_TEST: BIVARIATE_NORMAL_CDF_VALUES returns values of the bivariate normal CDF. X Y R F(R)(X,Y) -2.00000 1.00000 0.500000 0.226033E-01 -1.00000 1.00000 0.500000 0.154873 0.00000 1.00000 0.500000 0.468743 1.00000 1.00000 0.500000 0.745204 2.00000 1.00000 0.500000 0.831861 3.00000 1.00000 0.500000 0.841031 -0.200000 0.500000 -0.900000 0.137702 -0.200000 0.500000 -0.800000 0.162175 -0.200000 0.500000 -0.700000 0.182741 -0.200000 0.500000 -0.600000 0.201007 -0.200000 0.500000 -0.500000 0.217775 -0.200000 0.500000 -0.400000 0.233509 -0.200000 0.500000 -0.300000 0.248506 -0.200000 0.500000 -0.200000 0.262975 -0.200000 0.500000 -0.100000 0.277073 -0.200000 0.500000 0.00000 0.290926 -0.200000 0.500000 0.100000 0.304641 -0.200000 0.500000 0.200000 0.318311 -0.200000 0.500000 0.300000 0.332026 -0.200000 0.500000 0.400000 0.345869 -0.200000 0.500000 0.500000 0.359915 -0.200000 0.500000 0.600000 0.374221 -0.200000 0.500000 0.700000 0.388771 -0.200000 0.500000 0.800000 0.403277 -0.200000 0.500000 0.900000 0.416210 1.00000 0.500000 0.673000 0.650827 2.00000 1.00000 0.500000 0.831861 0.00000 0.00000 -1.00000 0.00000 0.00000 0.00000 -0.500000 0.166667 0.00000 0.00000 0.00000 0.250000 0.00000 0.00000 0.500000 0.333333 0.00000 0.00000 1.00000 0.500000 1.00000 1.00000 0.500000 0.745204 1.00000 -1.00000 0.500000 0.154873 -1.00000 1.00000 0.500000 0.154873 -1.00000 -1.00000 0.500000 0.625141E-01 1.00000 1.00000 0.500000 0.745204 1.00000 -1.00000 0.500000 0.154873 -1.00000 1.00000 0.500000 0.154873 -1.00000 -1.00000 0.500000 0.625141E-01 0.707107 0.707107 0.500000 0.633702 C8_LOG_VALUES_TEST: C8_LOG_VALUES returns values of the natural logarithm of a complex value. X LN(X) ( -2.00000 , -2.00000 ) ( 1.03972 , -2.35619 ) ( -2.00000 , 1.00000 ) ( 0.804719 , 2.67795 ) ( -1.00000 , -1.00000 ) ( 0.346574 , -2.35619 ) ( -1.00000 , 0.00000 ) ( 0.00000 , 3.14159 ) ( 0.00000 , -2.00000 ) ( 0.693147 , -1.57080 ) ( 0.00000 , -1.00000 ) ( 0.00000 , -1.57080 ) ( 0.00000 , 1.00000 ) ( 0.00000 , 1.57080 ) ( 0.00000 , 2.00000 ) ( 0.693147 , 1.57080 ) ( 1.00000 , -1.00000 ) ( 0.346574 , -0.785398 ) ( 1.00000 , 0.00000 ) ( 0.00000 , 0.00000 ) ( 2.00000 , -2.00000 ) ( 1.03972 , -0.785398 ) ( 2.00000 , 1.00000 ) ( 0.804719 , 0.463648 ) 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 returns values of the Cauchy Cumulative Density Function. MU SIGMA X CDF 1.00000 0.500000 1.00000 0.5000000000000000 1.00000 0.500000 2.00000 0.8524163823495667 1.00000 0.500000 3.00000 0.9220208696226307 1.00000 0.500000 4.00000 0.9474315432887466 1.00000 2.00000 2.00000 0.6475836176504333 1.00000 3.00000 2.00000 0.6024163823495667 1.00000 4.00000 2.00000 0.5779791303773693 1.00000 5.00000 2.00000 0.5628329581890013 2.00000 2.00000 3.00000 0.6475836176504333 3.00000 2.00000 3.00000 0.5000000000000000 4.00000 2.00000 3.00000 0.3524163823495667 5.00000 2.00000 3.00000 0.2500000000000000 CBRT_VALUES_TEST: CBRT_VALUES returns values of the cube root. X CBRT(X) 0.00000 0.000000000000000 -0.810000E-08 -0.2008298856338348E-02 0.900000E-01 0.4481404746557165 -0.100000 -0.4641588833612779 0.400000 0.7368062997280773 -1.00000 -1.000000000000000 2.00000 1.259921049894873 -3.00000 -1.442249570307408 3.14159 1.464591887561523 -19.0000 -2.668401648721945 29.0000 3.072316825685847 -71.0000 -4.140817749422853 97.0000 4.594700892207039 -0.123457E+09 -497.9338592181745 CHEBY_T_POLY_VALUES_TEST: CHEBY_T_POLY_VALUES returns values of the Chebyshev T polynomials. N X T(N)(X) -1 0.8000 0.000000000000000 0 0.8000 1.000000000000000 1 0.8000 0.8000000000000000 2 0.8000 0.2800000000000000 3 0.8000 -0.3520000000000000 4 0.8000 -0.8431999999999999 5 0.8000 -0.9971200000000000 6 0.8000 -0.7521920000000000 7 0.8000 -0.2063872000000000 8 0.8000 0.4219724800000000 9 0.8000 0.8815431680000000 10 0.8000 0.9884965888000000 11 0.8000 0.7000513740800000 12 0.8000 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 0.8500 0.000000000000000 0 0.8500 1.000000000000000 1 0.8500 0.7000000000000000 2 0.8500 -0.2000000000000000E-01 3 0.8500 -0.7280000000000000 4 0.8500 -0.9992000000000000 5 0.8500 -0.6708800000000000 6 0.8500 0.5996800000000000E-01 7 0.8500 0.7548352000000000 8 0.8500 0.9968012800000000 9 0.8500 0.6406865920000000 10 0.8500 -0.9984005120000000E-01 11 0.8500 -0.7804626636799999 12 0.8500 -0.9928076779520000 7 0.000 -1.000000000000000 7 0.1000 0.2063872000000000 7 0.2000 -0.9784704000000000 7 0.3000 0.2580224000000000 7 0.4000 0.9870208000000000 7 0.5000 0.000000000000000 7 0.6000 -0.9870208000000000 7 0.7000 -0.2580224000000000 7 0.8000 0.9784704000000000 7 0.9000 -0.2063872000000000 7 1.000 1.000000000000000 CHEBY_U_POLY_VALUES_TEST: CHEBY_U_POLY_VALUES returns values of the Chebyshev U polynomials. N X U(N)(X) -1 0.8000 0.000000000000000 0 0.8000 1.000000000000000 1 0.8000 1.600000000000000 2 0.8000 1.560000000000000 3 0.8000 0.8960000000000000 4 0.8000 -0.1264000000000000 5 0.8000 -1.098240000000000 6 0.8000 -1.630784000000000 7 0.8000 -1.511014400000000 8 0.8000 -0.7868390400000000 9 0.8000 0.2520719360000000 10 0.8000 1.190154137600000 11 0.8000 1.652174684160000 12 0.8000 1.453325357056000 CHEBY_U01_POLY_VALUES_TEST: CHEBY_U01_POLY_VALUES returns values of the shifted Chebyshev U polynomials. N X U01(N)(X) -1 0.8500 0.000000000000000 0 0.8500 1.000000000000000 1 0.8500 1.400000000000000 2 0.8500 0.9600000000000000 3 0.8500 -0.5600000000000000E-01 4 0.8500 -1.038400000000000 5 0.8500 -1.397760000000000 6 0.8500 -0.9184639999999999 7 0.8500 0.1119104000000000 8 0.8500 1.075138560000000 9 0.8500 1.393283584000000 10 0.8500 0.8754584576000000 11 0.8500 -0.1676417433600000 12 0.8500 -1.110156898304000 7 0.000 -8.000000000000000 7 0.1000 1.511014400000000 7 0.2000 -1.133260800000000 7 0.3000 -0.1636352000000000 7 0.4000 1.019801600000000 7 0.5000 0.000000000000000 7 0.6000 -1.019801600000000 7 0.7000 0.1636352000000000 7 0.8000 1.133260800000000 7 0.9000 -1.511014400000000 7 1.000 8.000000000000000 CHEBY_V_POLY_VALUES_TEST: CHEBY_V_POLY_VALUES returns values of the Chebyshev V polynomials. N X V(N)(X) -1 0.8000 0.000000000000000 0 0.8000 1.000000000000000 1 0.8000 0.6000000000000000 2 0.8000 -0.4000000000000000E-01 3 0.8000 -0.6640000000000000 4 0.8000 -1.022400000000000 5 0.8000 -0.9718400000000000 6 0.8000 -0.5325440000000000 7 0.8000 0.1197696000000000 8 0.8000 0.7241753600000000 9 0.8000 1.038910976000000 10 0.8000 0.9380822016000000 11 0.8000 0.4620205465600000 12 0.8000 -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 0.8500 0.000000000000000 0 0.8500 1.000000000000000 1 0.8500 0.4000000000000000 2 0.8500 -0.4400000000000000 3 0.8500 -1.016000000000000 4 0.8500 -0.9824000000000001 5 0.8500 -0.3593600000000000 6 0.8500 0.4792960000000000 7 0.8500 1.030374400000000 8 0.8500 0.9632281600000000 9 0.8500 0.3181450240000000 10 0.8500 -0.5178251264000000 11 0.8500 -1.043100200960000 12 0.8500 -0.9425151549440000 7 0.000 -15.00000000000000 7 0.1000 3.141798400000000 7 0.2000 -1.391244800000000 7 0.3000 -1.217779200000000 7 0.4000 1.183705600000000 7 0.5000 1.000000000000000 7 0.6000 -0.8558976000000000 7 0.7000 -0.8905088000000000 7 0.8000 0.8752768000000000 7 0.9000 0.1197696000000000 7 1.000 1.000000000000000 CHEBY_W_POLY_VALUES_TEST: CHEBY_W_POLY_VALUES returns values of the Chebyshev W polynomials. N X W(N)(X) -1 0.8000 0.000000000000000 0 0.8000 1.000000000000000 1 0.8000 2.600000000000000 2 0.8000 3.160000000000000 3 0.8000 2.456000000000000 4 0.8000 0.7696000000000000 5 0.8000 -1.224640000000000 6 0.8000 -2.729024000000000 7 0.8000 -3.141798400000000 8 0.8000 -2.297853440000000 9 0.8000 -0.5347671040000000 10 0.8000 1.442226073600000 11 0.8000 2.842328821760000 12 0.8000 3.105500041216000 CHEBY_W01_POLY_VALUES_TEST: CHEBY_W01_POLY_VALUES returns values of the shifted Chebyshev W polynomials. N X W01(N)(X) -1 0.8500 0.000000000000000 0 0.8500 1.000000000000000 1 0.8500 2.400000000000000 2 0.8500 2.360000000000000 3 0.8500 0.9040000000000000 4 0.8500 -1.094400000000000 5 0.8500 -2.436160000000000 6 0.8500 -2.316224000000000 7 0.8500 -0.8065536000000000 8 0.8500 1.187048960000000 9 0.8500 2.468422144000000 10 0.8500 2.268742041600000 11 0.8500 0.7078167142400000 12 0.8500 -1.277798641664000 7 0.000 -1.000000000000000 7 0.1000 -0.1197696000000000 7 0.2000 -0.8752768000000000 7 0.3000 0.8905088000000000 7 0.4000 0.8558976000000000 7 0.5000 -1.000000000000000 7 0.6000 -1.183705600000000 7 0.7000 1.217779200000000 7 0.8000 1.391244800000000 7 0.9000 -3.141798400000000 7 1.000 15.00000000000000 CHI_VALUES_TEST: CHI_VALUES returns values of the Hyperbolic Cosine Integral function CHI(X). X CHI(X) 0.500000 -0.5277684495649362E-01 0.600000 0.1577508933739787 0.700000 0.3455691756953907 0.800000 0.5183999848333914 0.900000 0.6813138871854340 1.00000 0.8378669409802082 1.20000 1.141841924170595 1.40000 1.445494075789644 1.60000 1.759505807660965 1.80000 2.092577214062032 2.00000 2.452666922646915 2.50000 3.524425488354165 3.00000 4.960392094765610 3.50000 6.959191927647393 4.00000 9.813547558823187 4.50000 13.96581164859243 CHI_SQUARE_CDF_VALUES_TEST: CHI_SQUARE_CDF_VALUES returns values of the Chi-Squared Cumulative Density Function. N X CDF 1 0.1000E-01 0.7965567455405796E-01 2 0.1000E-01 0.4987520807317687E-02 1 0.2000E-01 0.1124629160182849 2 0.2000E-01 0.9950166250831945E-02 1 0.4000 0.4729107431344619 2 0.4000 0.1812692469220181 3 0.4000 0.5975750516063926E-01 4 0.4000 0.1752309630642177E-01 1 1.000 0.6826894921370859 2 1.000 0.3934693402873666 3 1.000 0.1987480430987992 4 1.000 0.9020401043104986E-01 5 1.000 0.3743422675270363E-01 3 2.000 0.4275932955291202 3 3.000 0.6083748237289111 3 4.000 0.7385358700508894 3 5.000 0.8282028557032669 3 6.000 0.8883897749052874 10 1.000 0.1721156299558408E-03 10 2.000 0.3659846827343712E-02 10 3.000 0.1857593622214067E-01 CHI_SQUARE_PDF_VALUES_TEST: CHI_SQUARE_PDF_VALUES returns values of the Chi-Squared Probability Density Function. DF X PDF 1.000 0.1000E-01 3.969525474770117 2.000 0.1000E-01 0.4975062395963412 1.000 0.2000E-01 2.792879016972342 2.000 0.2000E-01 0.4950249168745841 1.000 0.4000 0.5164415474672784 2.000 0.4000 0.4093653765389909 3.000 0.4000 0.2065766189869113 4.000 0.4000 0.8187307530779819E-01 1.000 1.000 0.2419707245191434 2.000 1.000 0.3032653298563167 3.000 1.000 0.2419707245191434 4.000 1.000 0.1516326649281584 5.000 1.000 0.8065690817304777E-01 3.000 2.000 0.2075537487102974 3.000 3.000 0.1541803298037693 3.000 4.000 0.1079819330263761 3.000 5.000 0.7322491280963248E-01 3.000 6.000 0.4865217332964145E-01 10.00 1.000 0.7897534631674914E-03 10.00 2.000 0.7664155024405050E-02 10.00 3.000 0.2353325907815472E-01 CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST: CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral Chi-Squared Cumulative Density Function. DF LAMBDA X CDF 1 0.5000 3.000 0.8399444269398261 2 0.5000 3.000 0.6959060300435139 3 0.5000 3.000 0.5350879697078847 1 1.000 3.000 0.7647841496310313 2 1.000 3.000 0.6206436532195436 3 1.000 3.000 0.4691667375373180 1 5.000 3.000 0.3070884345937569 2 5.000 3.000 0.2203818092990903 3 5.000 3.000 0.1500251895581519 1 20.00 3.000 0.3071163194335791E-02 2 20.00 3.000 0.1763982670131894E-02 3 20.00 3.000 0.9816792594625021E-03 60 30.00 60.00 0.1651753140866208E-01 80 30.00 60.00 0.2023419573950451E-03 100 30.00 60.00 0.4984476352854074E-06 1 5.000 0.5000E-01 0.1513252400654827E-01 2 5.000 0.5000E-01 0.2090414910614367E-02 3 5.000 0.5000E-01 0.2465021206048452E-03 10 2.000 4.000 0.2636835050342939E-01 10 3.000 4.000 0.1857983220079215E-01 10 4.000 4.000 0.1305736595486640E-01 10 2.000 5.000 0.5838039534819351E-01 10 3.000 5.000 0.4249784402463712E-01 10 4.000 5.000 0.3082137716021596E-01 10 2.000 6.000 0.1057878223400849 10 3.000 6.000 0.7940842984598509E-01 10 4.000 6.000 0.5932010895599639E-01 8 0.5000 5.000 0.2110395656918684 CI_VALUES_TEST: CI_VALUES returns values of the Cosine Integral function CI(X). X CI(X) 0.500000 -0.1777840788066129 0.600000 -0.2227070695927976E-01 0.700000 0.1005147070088978 0.800000 0.1982786159524672 0.900000 0.2760678304677729 1.00000 0.3374039229009681 1.20000 0.4204591828942405 1.40000 0.4620065850946773 1.60000 0.4717325169318778 1.80000 0.4568111294183369 2.00000 0.4229808287748650 2.50000 0.2858711963653835 3.00000 0.1196297860080003 3.50000 -0.3212854851248112E-01 4.00000 -0.1409816978869304 4.50000 -0.1934911221017388 CIN_VALUES_TEST: CIN_VALUES returns values of the Cosine Integral function CIN(X). X CIN(X) 0.500000 0.6185256314820045E-01 0.600000 0.8866074809482194E-01 0.700000 0.1200260139539026 0.800000 0.1557934976348559 0.900000 0.1957873187759337 1.00000 0.2398117420005647 1.20000 0.3390780388012470 1.40000 0.4516813164280685 1.60000 0.5754867772153907 1.80000 0.7081912003853150 2.00000 0.8473820166866132 2.50000 1.207635200410304 3.00000 1.556198167561642 3.50000 1.862107181909382 4.00000 2.104491723908354 4.50000 2.274784183779546 CINH_VALUES_TEST: CINH_VALUES returns values of the Hyperbolic Cosine Integral function CINH(X). X CINH(X) 0.00000 0.000000000000000 0.500000 0.6315467070191882E-01 0.600000 0.9136085223843649E-01 0.700000 0.1250284547325902 0.800000 0.1643278712460683 0.900000 0.2094587379417273 1.00000 0.2606512760786754 1.20000 0.3823047024751071 1.40000 0.5318061742668980 1.60000 0.7122865135136963 1.80000 0.9275748842583805 2.00000 1.182304077185436 2.50000 2.030919091578478 3.00000 3.284564141195967 3.50000 5.129213294250493 4.00000 7.850037532801762 4.50000 11.88451858691463 CLAUSEN_VALUES_TEST: CLAUSEN_VALUES returns values of Clausen's integral. X FX 0.195312E-02 0.1413735288676058E-01 0.312500E-01 0.1395546708198128 -0.125000 -0.3849573215657424 0.500000 0.8483118777036792 1.00000 1.013959132360768 -1.50000 -0.9392185927540921 2.00000 0.7271460508632792 2.50000 0.4335982032355328 -3.00000 -0.9802620939130142E-01 4.00000 -0.5681439444298698 4.25000 -0.7096970178444892 -5.00000 0.9928201325469567 5.50000 -0.9812774747744737 6.00000 -0.6407826657017233 8.00000 0.8602796373323119 -10.0000 0.3907164760868021 15.0000 0.4757479392653919 20.0000 1.010501448141288 -30.0000 0.9633208904436308 50.0000 -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 1.000000000000000 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 returns values of the cosine function. X COS(X) 0.00000 1.000000000000000 0.261799 0.9659258262890683 0.500000 0.8775825618903728 0.523599 0.8660254037844386 0.785398 0.7071067811865476 1.00000 0.5403023058681398 1.04720 0.5000000000000000 1.57080 0.000000000000000 2.00000 -0.4161468365471424 3.00000 -0.9899924966004454 3.14159 -1.000000000000000 4.00000 -0.6536436208636119 5.00000 0.2836621854632262 COS_DEGREE_VALUES_TEST: COS_DEGREE_VALUES returns values of the cosine function. X COS_DEGREE(X) -5.00000 0.9961946980917455 0.00000 1.000000000000000 1.00000 0.9998476951563913 2.00000 0.9993908270190958 3.00000 0.9986295347545738 4.00000 0.9975640502598242 5.00000 0.9961946980917455 10.0000 0.9848077530122080 15.0000 0.9659258262890683 30.0000 0.8660254037844386 45.0000 0.7071067811865476 60.0000 0.5000000000000000 75.0000 0.2588190451025207 85.0000 0.8715574274765818E-01 86.0000 0.6975647374412530E-01 87.0000 0.5233595624294383E-01 88.0000 0.3489949670250097E-01 89.0000 0.1745240643728351E-01 90.0000 0.000000000000000 91.0000 -0.1745240643728351E-01 105.000 -0.2588190451025207 180.000 -1.000000000000000 COS_POWER_INT_VALUES_TEST: COS_POWER_INT_VALUES returns values of the integral of COS(X)^N from A to B. A B N COS_POWER_INT(A,B,N) 0.00000 3.14159 0 3.14159 0.00000 3.14159 1 0.00000 0.00000 3.14159 2 1.57080 0.00000 3.14159 3 0.00000 0.00000 3.14159 4 1.17810 0.00000 3.14159 5 0.00000 0.00000 3.14159 6 0.981748 0.00000 3.14159 7 0.00000 0.00000 3.14159 8 0.859029 0.00000 3.14159 9 0.00000 0.00000 3.14159 10 0.773126 COSH_VALUES_TEST: COSH_VALUES returns values of the hyperbolic cosine function. X COSH(X) -5.00000 74.20994852478785 -1.00000 1.543080634815244 0.00000 1.000000000000000 0.100000 1.005004168055804 0.200000 1.020066755619076 0.300000 1.045338514128860 0.400000 1.081072371838455 0.500000 1.127625965206381 0.600000 1.185465218242268 0.700000 1.255169005630943 0.800000 1.337434946304844 0.900000 1.433086385448774 1.00000 1.543080634815244 2.00000 3.762195691083631 3.00000 10.06766199577777 4.00000 27.30823283601649 5.00000 74.20994852478785 10.0000 11013.23292010332 COT_VALUES_TEST: COT_VALUES returns values of the cotangent function. X COT(X) 0.833333E-01 11.97220935362866 0.261799 3.732050807568877 0.500000 1.830487721712452 0.523599 1.732050807568877 0.785398 1.000000000000000 1.00000 0.6420926159343308 1.04720 0.5773502691896257 1.30900 0.2679491924311227 1.57080 0.000000000000000 1.43990 0.1316524975873959 1.50535 0.6554346281523823E-01 2.00000 -0.4576575543602858 3.00000 -7.015252551434534 4.00000 0.8636911544506166 5.00000 -0.2958129155327455 cp_values_test(): cp_values() returns values of the specific heat CP as a function of temperature and pressure. T P CP(T,P) 0.00000 1.00000 4.22800 100.000 1.00000 2.04200 200.000 1.00000 1.97500 300.000 1.00000 2.01300 350.000 1.00000 2.04000 400.000 1.00000 2.07000 500.000 1.00000 2.13500 600.000 1.00000 2.20300 850.000 1.00000 2.37800 1100.00 1.00000 2.54100 1600.00 1.00000 2.79200 2000.00 1.00000 2.93100 0.00000 5.00000 4.22600 0.00000 10.0000 4.22300 0.00000 50.0000 4.20200 0.00000 100.000 4.17700 0.00000 200.000 4.13000 0.00000 300.000 4.08900 0.00000 400.000 4.05300 0.00000 500.000 4.02100 0.00000 1000.00 3.90900 0.00000 1500.00 3.84400 0.00000 2000.00 3.78600 0.00000 5000.00 2.89000 datenum_values_test(): datenum_values() returns values of the MATLAB DATENUM for a given Y/M/D date. Y M D DATENUM 0 1 1 1. 1 1 1 367. 100 1 1 36526. 1000 1 1 ****** 1939 8 17 ****** 1944 9 9 ****** 1952 3 10 ****** 1966 5 12 ****** 1980 1 6 ****** 1996 2 25 ****** 2000 1 1 ****** dawson_values_test(): dawson_values() returns values of Dawson's Integral function. X DAWSON(X) 0.00000 0.000000000000000 0.100000 0.9933599239785286E-01 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 1.00000 0.5380795069127684 1.10000 0.5262066799705525 1.20000 0.5072734964077396 1.30000 0.4833975173848241 1.40000 0.4565072375268973 1.50000 0.4282490710853986 1.60000 0.3999398943230814 1.70000 0.3725593489740788 1.80000 0.3467727691148722 1.90000 0.3229743193228178 2.00000 0.3013403889237920 debye1_values_test(): debye1_values() returns values of Debye's function of order 1. X DEBYE1(X) 0.195312E-02 0.9995118247138088 0.312500E-01 0.9922146264712060 0.125000 0.9691839599789531 0.500000 0.8819271567906055 1.00000 0.7775046341122482 1.50000 0.6861453107894020 2.00000 0.6069472846098101 2.50000 0.5387895690778559 3.00000 0.4804352195730429 4.00000 0.3881480212979379 4.25000 0.3693080282924253 5.00000 0.3208761977001461 5.50000 0.2942399662315425 6.00000 0.2712604667850219 8.00000 0.2052393031022150 10.0000 0.1644434656799460 15.0000 0.1096619448273582 20.0000 0.8224670117820002E-01 30.0000 0.5483113556151085E-01 50.0000 0.3289868133696453E-01 debye2_values_test(): debye2_values() returns values of Debye's function of order 2. X DEBYE2(X) 0.195312E-02 0.9993491172790460 0.312500E-01 0.9896240229959918 0.125000 0.9589842620034599 0.500000 0.8437211933472536 1.00000 0.7078784756278292 1.50000 0.5914963722567128 2.00000 0.4930826439905319 2.50000 0.4107941357974967 3.00000 0.3426139606078635 4.00000 0.2405536875212790 4.25000 0.2208277006120231 5.00000 0.1723291593901414 5.50000 0.1472434673873018 6.00000 0.1266691904671579 8.00000 0.7426880595486285E-01 10.0000 0.4797149802012187E-01 15.0000 0.2136920168365837E-01 20.0000 0.1202056447644643E-01 30.0000 0.5342475124953707E-02 50.0000 0.1923291045055351E-02 debye3_values_test(): debye3_values() returns values of Debye's function of order 3. X DEBYE3(X) 0.195312E-02 0.9992677688598546 0.312500E-01 0.9883300775573470 0.125000 0.9539061047202351 0.500000 0.8249629689762337 1.00000 0.6744155640778147 1.50000 0.5471066514128629 2.00000 0.4411284737276242 2.50000 0.3541360348104239 3.00000 0.2835798281434225 4.00000 0.1817369138217748 4.25000 0.1627792438511244 5.00000 0.1175974117999340 5.50000 0.9524080272315889E-01 6.00000 0.7758132473376302E-01 8.00000 0.3656029567319485E-01 10.0000 0.1929576569034549E-01 15.0000 0.5771263227618880E-02 20.0000 0.2435220067480548E-02 30.0000 0.7215488221633566E-03 50.0000 0.1558545456544039E-03 debye4_values_test(): debye4_values() returns values of Debye's function of order 4. X DEBYE4(X) 0.195312E-02 0.9992189619276157 0.312500E-01 0.9875542528099607 0.125000 0.9508678860638974 0.500000 0.8138456917203404 1.00000 0.6548740688867369 1.50000 0.5216283096487871 2.00000 0.4118927367178853 2.50000 0.3229543485870731 3.00000 0.2518786364288331 4.00000 0.1518546125867202 4.25000 0.1337266114592141 5.00000 0.9147137766448117E-01 5.50000 0.7122782819746253E-01 6.00000 0.5567654782273886E-01 8.00000 0.2196756652557496E-01 10.0000 0.9673675560271159E-02 15.0000 0.1964697815835184E-02 20.0000 0.6221464862396545E-03 30.0000 0.1228951409207786E-03 50.0000 0.1592721031900216E-04 dedekind_sum_values_test(): dedekind_sum_values() returns values of the Dedekind sum function: (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() returns values of the dielectric function. T P EPS(T,P) 0.00000 100.000 88.2900 0.00000 500.000 90.0700 0.00000 1000.00 92.0200 0.00000 2000.00 95.1400 0.00000 5000.00 100.770 25.0000 100.000 78.8500 50.0000 100.000 70.2700 75.0000 100.000 62.6000 100.000 100.000 55.7800 150.000 100.000 44.3100 200.000 100.000 35.1100 300.000 100.000 20.4000 400.000 100.000 1.17000 500.000 100.000 1.11000 600.000 100.000 1.08000 dilogarithm_values_test(): dilogarithm_values() returns values of the dilogarithm function. X DILOGARITHM(X) 0.00000 0.000000000000000 0.500000E-01 0.5063929246449603E-01 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 1.074794600008248 0.850000 1.180581123830255 0.900000 1.299714723004959 0.950000 1.440633796970039 1.00000 1.644934066848226 dixon_elliptic_test(): dixon_elliptic() returns values of the Dixon elliptic functions cm(x) and sm(x). x cm(x) sm(x) cm(x)^3+sm(x)^3 0.00000 1.00000 0.00000 1.00000 0.100000 0.999667 0.999833E-01 1.00000 0.200000 0.997337 0.199734 1.00000 0.300000 0.991040 0.298657 0.999999 0.400000 0.978892 0.395785 1.00000 0.500000 0.959182 0.489826 1.00000 0.600000 0.930494 0.579255 1.00000 0.700000 0.891817 0.662445 0.999998 0.800000 0.842651 0.737828 1.00000 0.900000 0.783054 0.804069 1.00000 1.00000 0.713636 0.860228 1.00000 1.10000 0.635486 0.905873 1.00000 1.20000 0.550033 0.941134 0.999998 1.30000 0.458886 0.966693 1.00000 1.40000 0.363655 0.983705 0.999999 1.50000 0.265799 0.993701 1.00000 1.60000 0.166510 0.998459 1.00000 1.70000 0.666355E-01 0.999901 0.999999 1.80000 -0.333615E-01 1.00001 0.999993 1.90000 -0.133414 1.00079 0.999997 2.00000 -0.233857 1.00425 1.00001 e1_values_test(): e1_values() returns 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 1.00000 0.2193839343955203 1.10000 0.1859909045360402 1.20000 0.1584084368514626 1.30000 0.1354509578491291 1.40000 0.1162193125713579 1.50000 0.1000195824066327 1.60000 0.8630833369753979E-01 1.70000 0.7465464440125305E-01 1.80000 0.6471312936386886E-01 1.90000 0.5620437817453485E-01 2.00000 0.4890051070806112E-01 ei_values_test(): ei_values() returns values of the exponential integral function EI(X). X EI(X) 0.500000 0.4542199048631736 0.600000 0.7698812899373594 0.700000 1.064907194624291 0.800000 1.347396548212326 0.900000 1.622811713696867 1.00000 1.895117816355937 1.10000 2.167378279563403 1.20000 2.442092285192652 1.30000 2.721398880232024 1.40000 3.007207464150646 1.50000 3.301285449129798 1.60000 3.605319949019469 1.70000 3.920963201354904 1.80000 4.249867557487934 1.90000 4.593713686953585 2.00000 4.954234356001890 easter_gregorian_values_test(): easter_gregorian_values() returns values of the occurrence of Easter in the Gregorian calendar. D M Y 3 30 1997 4 12 1998 4 4 1999 4 23 2000 4 15 2001 3 31 2002 4 20 2003 4 11 2004 3 27 2005 4 16 2006 easter_julian_values_test(): easter_julian_values() returns values of the occurrence of Easter in the Julian calendar. D M Y 4 27 1997 4 19 1998 4 11 1999 4 30 2000 4 15 2001 5 5 2002 4 27 2003 4 11 2004 5 1 2005 4 23 2006 elliptic_ea_values_test(): elliptic_ea_values() returns values of the complete elliptic integral of the second kind, with parameter angle ALPHA in degrees. ALPHA E(ALPHA) 0.00000 1.570796326794897 5.00000 1.567809073977622 10.0000 1.558887196601596 15.0000 1.544150496914673 20.0000 1.523799205259774 25.0000 1.498114928422116 30.0000 1.467462209339427 35.0000 1.432290969306756 40.0000 1.393140248523812 45.0000 1.350643881047676 50.0000 1.305539094297794 55.0000 1.258679624779997 60.0000 1.211056027568459 65.0000 1.163827964493139 70.0000 1.118377737969864 75.0000 1.076405113076403 80.0000 1.040114395706010 85.0000 1.012663506234396 90.0000 1.000000000000000 elliptic_em_values_test(): elliptic_em_values() returns values of the complete elliptic integral of the second kind, with parameter K. K E(K) 0.00000 1.570796326794897 0.223607 1.550973351780472 0.316228 1.530757636897763 0.387298 1.510121832092819 0.447214 1.489035058095853 0.500000 1.467462209339427 0.547723 1.445363064412665 0.591608 1.422691133490879 0.632456 1.399392138897432 0.670820 1.375401971871116 0.707107 1.350643881047676 0.741620 1.325024497958230 0.774597 1.298428035046913 0.806226 1.270707479650149 0.836660 1.241670567945823 0.866025 1.211056027568459 0.894427 1.178489924327839 0.921954 1.143395791883166 0.948683 1.104774732704073 0.974679 1.060473727766278 1.00000 1.000000000000000 elliptic_em_values_test(): elliptic_em_values() returns values of the complete elliptic integral of the second kind, with parameter modulus M. M E(M) 0.00000 1.570796326794897 0.500000E-01 1.550973351780472 0.100000 1.530757636897763 0.150000 1.510121832092819 0.200000 1.489035058095853 0.250000 1.467462209339427 0.300000 1.445363064412665 0.350000 1.422691133490879 0.400000 1.399392138897432 0.450000 1.375401971871116 0.500000 1.350643881047676 0.550000 1.325024497958230 0.600000 1.298428035046913 0.650000 1.270707479650149 0.700000 1.241670567945823 0.750000 1.211056027568459 0.800000 1.178489924327839 0.850000 1.143395791883166 0.900000 1.104774732704073 0.950000 1.060473727766278 1.00000 1.000000000000000 elliptic_fa_values_test(): elliptic_fa_values() returns values of the complete elliptic integral of the first kind, with parameter angle ALPHA in degrees. ALPHA F(ALPHA) 0.00000 1.570796326794897 5.00000 1.573792130924768 10.0000 1.582842804338351 15.0000 1.598142002112540 20.0000 1.620025899124204 25.0000 1.648995218478530 30.0000 1.685750354812596 35.0000 1.731245175657058 40.0000 1.786769134885021 45.0000 1.854074677301372 50.0000 1.935581096004722 55.0000 2.034715312185791 60.0000 2.156515647499643 65.0000 2.308786798167196 70.0000 2.504550079001634 75.0000 2.768063145368768 80.0000 3.153385251887839 85.0000 3.831741999784146 elliptic_fk_values_test(): elliptic_fk_values() returns values of the complete elliptic integral of the first kind, with parameter K. K F(K) 0.00000 1.570796326794897 0.223607 1.591003453790792 0.316228 1.612441348720219 0.387298 1.635256732264580 0.447214 1.659623598610528 0.500000 1.685750354812596 0.547723 1.713889448178791 0.591608 1.744350597225613 0.632456 1.777519371491253 0.670820 1.813883936816983 0.707107 1.854074677301372 0.741620 1.898924910271554 0.774597 1.949567749806026 0.806226 2.007598398424376 0.836660 2.075363135292469 0.866025 2.156515647499643 0.894427 2.257205326820854 0.921954 2.389016486325580 0.948683 2.578092113348173 0.974679 2.908337248444552 elliptic_fm_values_test(): elliptic_fm_values() returns values of the complete elliptic integral of the first kind, with parameter modulus M. M F(M) 0.00000 1.570796326794897 0.500000E-01 1.591003453790792 0.100000 1.612441348720219 0.150000 1.635256732264580 0.200000 1.659623598610528 0.250000 1.685750354812596 0.300000 1.713889448178791 0.350000 1.744350597225613 0.400000 1.777519371491253 0.450000 1.813883936816983 0.500000 1.854074677301372 0.550000 1.898924910271554 0.600000 1.949567749806026 0.650000 2.007598398424376 0.700000 2.075363135292469 0.750000 2.156515647499643 0.800000 2.257205326820854 0.850000 2.389016486325580 0.900000 2.578092113348173 0.950000 2.908337248444552 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) 0.343091 8.450690 0.2732317284159052 1.302990 0.603988 1.1247497250997811 0.652363 0.179413 0.6446601913679151 0.404602 0.709569 0.3968902354370061 0.068846 133.964339 0.0606396079994467 0.096961 47.966214 0.0890941157794873 0.630370 2.172071 0.5324020148020150 1.252375 0.002038 1.2518886406602650 1.409796 0.360004 1.2889711619162600 0.148511 0.621954 0.1481718153599732 1.349466 0.883422 1.0380901856399130 0.193371 0.203429 0.1931275771541276 0.408883 5.772526 0.3304419611986801 0.178543 11.148539 0.1673947960639630 1.292588 0.288924 1.2145011753247359 1.087096 0.716662 0.9516560179840655 1.352795 0.476062 1.2036829595261760 1.432530 0.609495 1.2064263261854189 0.296809 8.902277 0.2522791382096692 0.623588 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 returns values of the complete elliptic integral of the third kind, with parameter angle A in degrees. N A Pi(N,A) -10.0000 30.0000 0.4892245275965397 -10.0000 45.0000 0.5106765677902629 -10.0000 60.0000 0.5460409271920561 -10.0000 77.0790 0.6237325893535237 -3.00000 30.0000 0.8230455426606750 -3.00000 45.0000 0.8760028274011437 -3.00000 60.0000 0.9660073560143946 -3.00000 77.0790 1.171952391481798 -1.00000 30.0000 1.177446843000566 -1.00000 45.0000 1.273127366749682 -1.00000 60.0000 1.440034318657551 -1.00000 77.0790 1.836472172302591 0.00000 30.0000 1.685750354812596 0.00000 45.0000 1.854074677301372 0.00000 60.0000 2.156515647499643 0.00000 77.0790 2.908337248444552 0.500000 30.0000 2.413671504201195 0.500000 45.0000 2.701287762095351 0.500000 60.0000 3.234773471249465 0.500000 77.0790 4.633308147279891 ELLIPTIC_PIK_VALUES_TEST: ELLIPTIC_PIK_VALUES returns values of the complete elliptic integral of the third kind, with parameter K. N K Pi(N,K) -10.0000 0.500000 0.4892245275965397 -10.0000 0.707107 0.5106765677902629 -10.0000 0.866025 0.5460409271920561 -10.0000 0.974679 0.6237325893535237 -3.00000 0.500000 0.8230455426606750 -3.00000 0.707107 0.8760028274011437 -3.00000 0.866025 0.9660073560143946 -3.00000 0.974679 1.171952391481798 -1.00000 0.500000 1.177446843000566 -1.00000 0.707107 1.273127366749682 -1.00000 0.866025 1.440034318657551 -1.00000 0.974679 1.836472172302591 0.00000 0.500000 1.685750354812596 0.00000 0.707107 1.854074677301372 0.00000 0.866025 2.156515647499643 0.00000 0.974679 2.908337248444552 0.500000 0.500000 2.413671504201195 0.500000 0.707107 2.701287762095351 0.500000 0.866025 3.234773471249465 0.500000 0.974679 4.633308147279891 ELLIPTIC_PIM_VALUES_TEST: ELLIPTIC_PIM_VALUES returns values of the complete elliptic integral of the third kind, with parameter M. N M Pi(N,M) -10.0000 0.250000 0.4892245275965397 -10.0000 0.500000 0.5106765677902629 -10.0000 0.750000 0.5460409271920561 -10.0000 0.950000 0.6237325893535237 -3.00000 0.250000 0.8230455426606750 -3.00000 0.500000 0.8760028274011437 -3.00000 0.750000 0.9660073560143946 -3.00000 0.950000 1.171952391481798 -1.00000 0.250000 1.177446843000566 -1.00000 0.500000 1.273127366749682 -1.00000 0.750000 1.440034318657551 -1.00000 0.950000 1.836472172302591 0.00000 0.250000 1.685750354812596 0.00000 0.500000 1.854074677301372 0.00000 0.750000 2.156515647499643 0.00000 0.950000 2.908337248444552 0.500000 0.250000 2.413671504201195 0.500000 0.500000 2.701287762095351 0.500000 0.750000 3.234773471249465 0.500000 0.950000 4.633308147279891 ERF_VALUES_TEST: ERF_VALUES returns values of the error function ERF(X). X ERF(X) 0.00000 0.000000000000000 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 1.00000 0.8427007929497149 1.10000 0.8802050695740817 1.20000 0.9103139782296354 1.30000 0.9340079449406524 1.40000 0.9522851197626488 1.50000 0.9661051464753106 1.60000 0.9763483833446440 1.70000 0.9837904585907746 1.80000 0.9890905016357306 1.90000 0.9927904292352575 2.00000 0.9953222650189527 ERFC_VALUES_TEST: ERFC_VALUES returns values of the complementary error function ERFC(X). X ERFC(X) 0.00000 1.000000000000000 0.200000 0.7772974107895215 0.400000 0.5716076449533315 0.600000 0.3961439091520741 0.800000 0.2578990352923395 1.00000 0.1572992070502851 1.20000 0.8968602177036462E-01 1.40000 0.4771488023735119E-01 1.60000 0.2365161665535599E-01 1.80000 0.1090949836426929E-01 2.00000 0.4677734981047266E-02 2.20000 0.1862846297981891E-02 2.40000 0.6885138966450786E-03 2.60000 0.2360344165293492E-03 2.80000 0.7501319466545903E-04 3.00000 0.2209049699858544E-04 3.20000 0.6025761151762095E-05 3.40000 0.1521993362862285E-05 3.60000 0.3558629930076853E-06 3.80000 0.7700392745696413E-07 4.00000 0.1541725790028002E-07 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 returns values of the Euler polynomials. N X EULER_POLY(N,X) 0 0.200000 1.000000000000000 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 1.718788800000000 8 0.200000 3.180431360000000 9 0.200000 -12.53946700800000 10 0.200000 -28.99993845760000 5 -0.500000 -0.6250000000000000E-01 5 -0.400000 -0.1742400000000000 5 -0.300000 -0.2976800000000000 5 -0.200000 -0.4043200000000000 5 -0.100000 -0.4752600000000000 5 0.00000 -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 0.000000000000000 5 0.600000 0.1537600000000000 5 0.700000 0.2928200000000000 5 0.800000 0.4036800000000000 5 0.900000 0.4752400000000000 5 1.00000 0.5000000000000000 EXP_VALUES_TEST: EXP_VALUES returns values of the exponential function. X EXP(X) -10.0000 0.4539992976248485E-04 -5.00000 0.6737946999085467E-02 -1.00000 0.3678794411714423 0.00000 1.000000000000000 0.100000E-07 1.000000010000000 0.100000E-03 1.000100005000167 0.100000E-02 1.001000500166708 0.100000E-01 1.010050167084168 0.100000 1.105170918075648 0.200000 1.221402758160170 0.300000 1.349858807576003 0.400000 1.491824697641270 0.500000 1.648721270700128 0.600000 1.822118800390509 0.700000 2.013752707470477 0.800000 2.225540928492467 0.900000 2.459603111156950 1.00000 2.718281828459045 2.00000 7.389056098930650 3.14159 23.14069263277927 5.00000 148.4131591025766 10.0000 22026.46579480672 20.0000 485165195.4097903 40.0000 0.2353852668370200E+18 EXP3_INT_VALUES_TEST: EXP3_INT_VALUES returns values of the EXP3 Integral function. X EXP3_INT(X) 0.195312E-02 0.1953124996362021E-02 0.781250E-02 0.7812499068677552E-02 0.312500E-01 0.3124976158349973E-01 0.125000 0.1249389988880308 0.500000 0.4849171431136397 1.00000 0.8075111821396714 1.25000 0.8688926541262327 1.50000 0.8886172223535717 1.87500 0.8928601850021818 2.00000 0.8929535142938763 2.12500 0.8929747911273784 2.25000 0.8929788057979812 2.50000 0.8929795031749662 2.75000 0.8929795115295190 3.00000 0.8929795115691812 3.12500 0.8929795115692474 3.25000 0.8929795115692492 3.50000 0.8929795115692493 3.75000 0.8929795115692493 4.00000 0.8929795115692493 EXPONENTIAL_01_PDF_VALUES_TEST: EXPONENTIAL_01_PDF_VALUES returns values of the standard Exponential PDF. X PDF 0.701301 0.4959398481993681 4.75975 0.8567779591356970E-02 4.06230 0.1720937842266235E-01 2.58932 0.7507070056996956E-01 1.78419 0.1679332083261492 -0.136347 0.000000000000000 0.916678 0.3998451794786390 0.104762 0.9005384971416223 -0.258941 0.000000000000000 2.98681 0.5044803826563792E-01 EXPONENTIAL_CDF_VALUES_TEST: EXPONENTIAL_CDF_VALUES returns values of the Exponential CDF. LAMBDA X CDF 0.500000 1.00000 0.3934693402873666 0.500000 2.00000 0.6321205588285577 0.500000 3.00000 0.7768698398515702 0.500000 4.00000 0.8646647167633873 1.00000 2.00000 0.8646647167633873 2.00000 2.00000 0.9816843611112658 3.00000 2.00000 0.9975212478233336 4.00000 2.00000 0.9996645373720975 5.00000 2.00000 0.9999546000702375 EXPONENTIAL_PDF_VALUES_TEST: EXPONENTIAL_PDF_VALUES returns values of the Exponential PDF. LAMBDA X CDF 1.09209 9.55881 0.1446999730194618E-03 4.14755 5.57312 0.6289850821824726E-01 2.07654 0.567799 0.3663607831924032 1.28789 1.01056 0.3542787877169571 0.219145 6.30305 0.1472582451176006E-11 0.308636 4.44034 0.1829637907028298E-05 2.00653 7.52220 0.1173398427218792E-01 3.98643 -0.814325E-01 0.000000000000000 4.48752 3.44260 0.1034724689882351 0.472724 0.375306E-01 1.953947804368330 EXTREME_VALUES_CDF_VALUES_TEST: EXTREME_VALUES_CDF_VALUES returns values of the Extreme Values Cumulative Density Function. ALPHA BETA X CDF 1.00000 0.500000 1.00000 0.3678794411714423 1.00000 0.500000 2.00000 0.8734230184931167 1.00000 0.500000 3.00000 0.9818510730616665 1.00000 0.500000 4.00000 0.9975243173927525 1.00000 2.00000 2.00000 0.5452392118926050 1.00000 3.00000 2.00000 0.4884435800065159 1.00000 4.00000 2.00000 0.4589560693076638 1.00000 5.00000 2.00000 0.4409910259429826 2.00000 2.00000 3.00000 0.5452392118926050 3.00000 2.00000 3.00000 0.3678794411714423 4.00000 2.00000 3.00000 0.1922956455479649 5.00000 2.00000 3.00000 0.6598803584531254E-01 F_CDF_VALUES_TEST: F_CDF_VALUES returns values of the F cumulative density function. A B X CDF 1 1 1.00000 0.5000000000000000 1 5 0.528000 0.4999714850534485 5 1 1.89000 0.4996034370170990 1 5 1.69000 0.7496993658293228 2 10 1.60000 0.7504656462757382 4 20 1.47000 0.7514156325324275 1 5 4.06000 0.8999867031372156 6 6 3.05000 0.8997127554259698 8 16 2.09000 0.9002845660853669 1 5 6.61000 0.9500248817817623 3 10 3.71000 0.9500574946122442 6 12 3.00000 0.9501926400000000 1 5 10.0100 0.9750133887312993 1 5 16.2600 0.9900022327445249 1 5 22.7800 0.9949977837872073 1 5 47.1800 0.9989999621122122 2 5 1.00000 0.5687988496283078 3 5 1.00000 0.5351452100063649 4 5 1.00000 0.5143428032407864 5 5 1.00000 0.5000000000000000 F_NONCENTRAL_CDF_VALUES_TEST: F_NONCENTRAL_CDF_VALUES returns values of the F cumulative density function. A B LAMBDA X CDF 1 1 0.000000 1.00000 0.500000 1 5 0.000000 1.00000 0.636783 1 5 0.250000 1.00000 0.584092 1 5 1.000000 0.500000 0.323443 1 5 1.000000 1.00000 0.450119 1 5 1.000000 2.00000 0.607888 1 5 1.000000 3.00000 0.705928 1 5 1.000000 4.00000 0.772178 1 5 1.000000 5.00000 0.819105 1 5 2.000000 1.00000 0.317035 2 5 1.000000 1.00000 0.432722 2 10 1.000000 1.00000 0.450270 3 5 1.000000 1.00000 0.426188 3 5 2.000000 1.00000 0.675369 4 5 1.000000 1.00000 0.422911 4 5 1.000000 2.00000 0.692767 5 1 0.000000 1.00000 0.363217 5 5 1.000000 1.00000 0.421005 6 6 1.000000 1.00000 0.426667 6 12 1.000000 1.00000 0.446402 8 16 1.000000 2.00000 0.844589 16 8 1.000000 2.00000 0.433930 factorial_values_test(): 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 factorial2_values_test(): 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 FRESNEL_COS_VALUES_TEST: FRESNEL_COS_VALUES returns values of the Fresnel cosine integral C(X). X C(X) 0.00000 0.000000000000000 0.200000 0.1999210575944531 0.400000 0.3974807591723594 0.600000 0.5810954469916523 0.800000 0.7228441718963561 1.00000 0.7798934003768228 1.20000 0.7154377229230734 1.40000 0.5430957835462564 1.60000 0.3654616834404877 1.80000 0.3336329272215571 2.00000 0.4882534060753408 2.20000 0.6362860449033195 2.40000 0.5549614058564281 2.60000 0.3889374961919690 2.80000 0.4674916516989059 3.00000 0.6057207892976856 FRESNEL_SIN_VALUES_TEST: FRESNEL_SIN_VALUES returns values of the Fresnel sine integral S(X). X S(X) 0.00000 0.000000000000000 0.200000 0.4187609161656762E-02 0.400000 0.3335943266061318E-01 0.600000 0.1105402073593870 0.800000 0.2493413930539178 1.00000 0.4382591473903548 1.20000 0.6234009185462497 1.40000 0.7135250773634121 1.60000 0.6388876835093809 1.80000 0.4509387692675831 2.00000 0.3434156783636982 2.20000 0.4557046121246569 2.40000 0.6196899649456836 2.60000 0.5499893231527195 2.80000 0.3915284435431718 3.00000 0.4963129989673750 FROBENIUS_NUMBER_DATA_VALUES_TEST: FROBENIUS_NUMBER_DATA_VALUES returns the corresponding coin denominations 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_ORDER_VALUES_TEST: FROBENIUS_NUMBER_ORDER_VALUES returns the order for a Frobenius problem; Problem Order 1 2 2 2 3 2 4 2 5 2 6 2 7 3 8 3 9 3 10 4 11 4 12 5 13 5 14 5 15 6 16 6 17 6 18 7 19 8 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 returns values of the Gamma function. X GAMMA(X) -0.500000 -3.544907701811032 -0.100000E-01 -100.5871979644108 0.100000E-01 99.43258511915060 0.100000 9.513507698668732 0.200000 4.590843711998803 0.400000 2.218159543757688 0.500000 1.772453850905516 0.600000 1.489192248812817 0.800000 1.164229713725303 1.00000 1.000000000000000 1.10000 0.9513507698668732 1.20000 0.9181687423997607 1.30000 0.8974706963062772 1.40000 0.8872638175030753 1.50000 0.8862269254527581 1.60000 0.8935153492876903 1.70000 0.9086387328532904 1.80000 0.9313837709802427 1.90000 0.9617658319073874 2.00000 1.000000000000000 3.00000 2.000000000000000 4.00000 6.000000000000000 10.0000 362880.0000000000 20.0000 0.1216451004088320E+18 30.0000 0.8841761993739702E+31 GAMMA_01_PDF_VALUES_TEST: GAMMA_01_PDF_VALUES returns values of the standard Gamma Probability Density Function. ALPHA X PDF 1.09209 9.54133 0.9260811963612823E-04 4.14755 5.39780 0.1260335478747823 2.07654 0.194247 0.1363536772414351 1.28789 0.654546 0.5114450139194701 0.219145 6.15664 0.1230139468263628E-03 0.308636 4.22016 0.1870342832511005E-02 2.00653 7.42407 0.4476000451227789E-02 3.98643 -0.480697 0.000000000000000 4.48752 3.18290 0.2056668486524041 0.472724 -0.357023 0.000000000000000 GAMMA_CDF_VALUES_TEST: GAMMA_CDF_VALUES returns values of the GAMMA Cumulative Density Function. MU SIGMA X CDF 1.00000 0.500000 1.00000 0.8646647167633873 1.00000 0.500000 2.00000 0.9816843611112658 1.00000 0.500000 3.00000 0.9975212478233336 1.00000 0.500000 4.00000 0.9996645373720975 1.00000 2.00000 2.00000 0.6321205588285577 1.00000 3.00000 2.00000 0.4865828809674080 1.00000 4.00000 2.00000 0.3934693402873666 1.00000 5.00000 2.00000 0.3296799539643607 2.00000 2.00000 3.00000 0.4421745996289254 3.00000 2.00000 3.00000 0.1911531694619419 4.00000 2.00000 3.00000 0.6564245437845009E-01 5.00000 2.00000 3.00000 0.1857593622214067E-01 GAMMA_INC_VALUES_TEST: GAMMA_INC_VALUES returns values of the incomplete Gamma function. A X GAMMA_INC(A)(X) 0.100000 0.300000E-01 2.490302836300570 0.100000 0.300000 0.8718369702247978 0.100000 1.50000 0.1079213896175866 0.500000 0.750000E-01 1.238121685818417 0.500000 0.750000 0.3911298052193973 0.500000 3.50000 0.1444722098952533E-01 1.00000 0.100000 0.9048374180359596 1.00000 1.00000 0.3678794411714423 1.00000 5.00000 0.6737946999085467E-02 1.10000 0.100000 0.8827966752611692 1.10000 1.00000 0.3908330082003269 1.10000 5.00000 0.8051456628620992E-02 2.00000 0.150000 0.9898141728888165 2.00000 1.50000 0.5578254003710746 2.00000 7.00000 0.7295055724436130E-02 6.00000 2.50000 114.9574754165633 6.00000 12.0000 2.440923530031405 11.0000 16.0000 280854.6620274718 26.0000 25.0000 0.8576480283455533E+25 41.0000 45.0000 0.2085031346403364E+48 GAMMA_INC_P_VALUES_TEST: GAMMA_INC_P_VALUES returns values of the incomplete Gamma function. A X GAMMA_INC_P(A)(X) 0.100000 0.300000E-01 0.7382350532339351 0.100000 0.300000 0.9083579897300343 0.100000 1.50000 0.9886559833621947 0.500000 0.750000E-01 0.3014646416966613 0.500000 0.750000 0.7793286380801532 0.500000 3.50000 0.9918490284064972 1.00000 0.100000 0.9516258196404043E-01 1.00000 1.00000 0.6321205588285577 1.00000 5.00000 0.9932620530009145 1.10000 0.100000 0.7205974576054322E-01 1.10000 1.00000 0.5891809618706485 1.10000 5.00000 0.9915368159845525 2.00000 0.150000 0.1018582711118352E-01 2.00000 1.50000 0.4421745996289254 2.00000 7.00000 0.9927049442755639 6.00000 2.50000 0.4202103819530612E-01 6.00000 12.0000 0.9796589705830716 11.0000 16.0000 0.9226039842296428 26.0000 25.0000 0.4470785799755852 41.0000 45.0000 0.7444549220718699 GAMMA_INC_Q_VALUES_TEST: GAMMA_INC_Q_VALUES returns values of the incomplete Gamma function. A X GAMMA_INC_Q(A)(X) 0.100000 0.300000E-01 0.2617649467660649 0.100000 0.300000 0.9164201026996573E-01 0.100000 1.50000 0.1134401663780527E-01 0.500000 0.750000E-01 0.6985353583033387 0.500000 0.750000 0.2206713619198468 0.500000 3.50000 0.8150971593502700E-02 1.00000 0.100000 0.9048374180359596 1.00000 1.00000 0.3678794411714423 1.00000 5.00000 0.6737946999085467E-02 1.10000 0.100000 0.9279402542394568 1.10000 1.00000 0.4108190381293515 1.10000 5.00000 0.8463184015447498E-02 2.00000 0.150000 0.9898141728888165 2.00000 1.50000 0.5578254003710746 2.00000 7.00000 0.7295055724436130E-02 6.00000 2.50000 0.9579789618046939 6.00000 12.0000 0.2034102941692837E-01 11.0000 16.0000 0.7739601577035708E-01 26.0000 25.0000 0.5529214200244148 41.0000 45.0000 0.2555450779281301 GAMMA_INC_TRICOMI_VALUES_TEST: GAMMA_INC_TRICOMI_VALUES returns values of the incomplete Gamma function. A X GAMMA_INC_TRICOMI(A)(X) 0.100000 0.300000E-01 1.048292641463504 0.100000 0.300000 1.024577737369574 0.100000 1.50000 0.9493712443185374 0.500000 0.750000E-01 1.100793230316492 0.500000 0.750000 0.8998911979655217 0.500000 3.50000 0.5301656062431039 1.00000 0.100000 0.9516258196404043 1.00000 1.00000 0.6321205588285577 1.00000 5.00000 0.1986524106001829 1.10000 0.100000 0.9071784510537487 1.10000 1.00000 0.5891809618706485 1.10000 5.00000 0.1688269752193589 2.00000 0.150000 0.4527034271637121 2.00000 1.50000 0.1965220442795224 2.00000 7.00000 0.2025928457705232E-01 6.00000 2.50000 0.1721181724479739E-03 6.00000 12.0000 0.3280858070850586E-06 11.0000 16.0000 0.5244396471821590E-13 26.0000 25.0000 0.2013462926183376E-36 41.0000 45.0000 0.1230623887499875E-67 GAMMA_LOG_VALUES_TEST: GAMMA_LOG_VALUES returns values of the logarithm of the Gamma function. X GAMMA_LOG(X) 0.200000 1.524063822430784 0.400000 0.7966778177017837 0.600000 0.3982338580692348 0.800000 0.1520596783998375 1.00000 0.000000000000000 1.10000 -0.4987244125983972E-01 1.20000 -0.8537409000331583E-01 1.30000 -0.1081748095078604 1.40000 -0.1196129141723712 1.50000 -0.1207822376352452 1.60000 -0.1125917656967557 1.70000 -0.9580769740706586E-01 1.80000 -0.7108387291437215E-01 1.90000 -0.3898427592308333E-01 2.00000 0.000000000000000 3.00000 0.6931471805599453 4.00000 1.791759469228055 10.0000 12.80182748008147 20.0000 39.33988418719949 30.0000 71.25703896716801 GAMMA_PDF_VALUES_TEST: GAMMA_PDF_VALUES returns values of a Gamma Probability Density Function. BETA ALPHA X PDF 1.09209 4.78159 4.94296 0.1672017697220646 2.80848 2.07654 0.209936 0.8522122814089312 1.28789 0.549784 0.717398E-01 2.122272611165834 3.16983 0.308636 2.58714 0.6993771842317114E-04 2.00653 3.77337 4.74318 0.1679379733182281E-01 0.919186E-02 4.48752 1.97466 0.6687464259463117E-09 0.472724 0.680845E-01 5.12640 0.1295436045931343E-02 4.20424 0.615520 -0.153423 0.000000000000000 1.30151 4.56242 0.504717 0.1189893036865762E-01 1.75814 4.11444 1.45622 0.3658836103539945 gcd_values_test(): gcd_values() returns values of the greatest common divisor function: m n gcd(m,n) 17 35 1 4 138322 2 291 294 3 100 64 4 55 625 5 30 66 6 2058 679 7 24 40 8 326880 131769 9 65610 146410 10 GEGENBAUER_POLY_VALUES_TEST: GEGENBAUER_POLY_VALUES returns values of the Gegenbauer polynomials. N A X G(N,A)(X) 0 0.5000 0.2000 1.00000 1 0.5000 0.2000 0.200000 2 0.5000 0.2000 -0.440000 3 0.5000 0.2000 -0.280000 4 0.5000 0.2000 0.232000 5 0.5000 0.2000 0.307520 6 0.5000 0.2000 -0.805760E-01 7 0.5000 0.2000 -0.293517 8 0.5000 0.2000 -0.395648E-01 9 0.5000 0.2000 0.245971 10 0.5000 0.2000 0.129072 2 0.000 0.4000 0.00000 2 1.000 0.4000 -0.360000 2 2.000 0.4000 -0.800000E-01 2 3.000 0.4000 0.840000 2 4.000 0.4000 2.40000 2 5.000 0.4000 4.60000 2 6.000 0.4000 7.44000 2 7.000 0.4000 10.9200 2 8.000 0.4000 15.0400 2 9.000 0.4000 19.8000 2 10.00 0.4000 25.2000 5 3.000 -.5000 -9.00000 5 3.000 -.4000 -0.161280 5 3.000 -.3000 -6.67296 5 3.000 -.2000 -8.37504 5 3.000 -.1000 -5.52672 5 3.000 0.000 0.00000 5 3.000 0.1000 5.52672 5 3.000 0.2000 8.37504 5 3.000 0.3000 6.67296 5 3.000 0.4000 0.161280 5 3.000 0.5000 -9.00000 5 3.000 0.6000 -15.4253 5 3.000 0.7000 -9.69696 5 3.000 0.8000 22.4410 5 3.000 0.9000 100.889 5 3.000 1.000 252.000 GEOMETRIC_CDF_VALUES_TEST: GEOMETRIC_CDF_VALUES returns values of the Geometric Probability Cumulative Density Function. X P CDF 1 0.1000 0.1900000000000000 2 0.1000 0.2710000000000000 3 0.1000 0.3439000000000000 10 0.1000 0.6861894039100001 1 0.2000 0.3600000000000000 2 0.2000 0.4880000000000000 3 0.2000 0.5904000000000000 10 0.2000 0.9141006540800000 3 0.3000 0.7599000000000000 3 0.4000 0.8704000000000000 3 0.5000 0.9375000000000000 5 0.5000 0.9843750000000000 10 0.5000 0.9995117187500000 3 0.9000 0.9999000000000000 GOODWIN_VALUES_TEST: GOODWIN_VALUES returns values of the Goodwin and Staton function. X F(X) 0.195312E-02 5.953154004044166 0.781250E-02 4.576960126862449 0.312500E-01 3.228892133190222 0.125000 1.974611087356872 0.500000 0.9635604620869773 1.00000 0.6051336525033446 1.25000 0.5130550645953220 1.50000 0.4459860282094613 1.87500 0.3734445820687975 2.00000 0.3543359288495306 2.12500 0.3371215651888192 2.50000 0.2943617072936298 3.00000 0.2519349964489722 3.50000 0.2202877822212394 4.00000 0.1957525823769892 4.50000 0.1761630316667070 5.00000 0.1601546947966478 5.75000 0.1409611687619339 6.00000 0.1355498719104907 7.00000 0.1175160506008510 GUD_VALUES_TEST: GUD_VALUES returns values of the Gudermannian function. X GUD(X) -2.00000 -1.301760336046015 -1.00000 -0.8657694832396586 0.00000 0.000000000000000 0.100000 0.9983374879348662E-01 0.200000 0.1986798470079397 0.500000 0.4803810791337294 1.00000 0.8657694832396586 1.50000 1.131728345250509 2.00000 1.301760336046015 2.50000 1.406993568936154 3.00000 1.471304341117193 3.50000 1.510419907545700 4.00000 1.534169144334733 harmonic_values_test(): harmonic_values() returns values of the Harmonic number sequence. N H(N) 1 1.000000000000000 2 1.500000000000000 3 1.833333333333333 4 2.083333333333333 5 2.283333333333333 6 2.450000000000000 7 2.592857142857143 8 2.717857142857143 9 2.828968253968254 10 2.928968253968254 11 3.019877344877345 12 3.103210678210678 13 3.180133755133755 14 3.251562326562327 15 3.318228993228993 16 3.380728993228993 17 3.439552522640758 18 3.495108078196313 19 3.547739657143682 20 3.597739657143682 21 3.645358704762730 22 3.690813250217275 23 3.734291511086840 24 3.775958177753507 25 3.815958177753507 26 3.854419716215045 27 3.891456753252082 28 3.927171038966368 29 3.961653797587058 30 3.994987130920391 31 4.027245195436520 32 4.058495195436520 33 4.088798225739550 34 4.118209990445433 35 4.146781419016861 36 4.174559196794639 37 4.201586223821666 38 4.227902013295350 39 4.253543038936376 40 4.278543038936376 HERMITE_FUNCTION_VALUES_TEST: HERMITE_FUNCTION_VALUES returns values of the Hermite functions. N X Hf(N,X) 0 0.00000 0.7511255444649425 1 0.00000 0.000000000000000 2 0.00000 -0.5311259660135985 3 0.00000 0.000000000000000 4 0.00000 0.4599685791773266 5 0.00000 0.000000000000000 0 1.00000 0.4555806720113325 1 1.00000 0.6442883651134752 2 1.00000 0.3221441825567376 3 1.00000 -0.2630296236233334 4 1.00000 -0.4649750762925110 5 1.00000 -0.5881521185179581E-01 6 1.00000 0.3905052515434106 7 1.00000 0.2631861423064045 8 1.00000 -0.2336911435996523 9 1.00000 -0.3582973361472840 10 1.00000 0.6146344487883041E-01 11 1.00000 0.3678312067984882 12 1.00000 0.9131969309166278E-01 5 0.500000 0.4385750950032321 5 2.00000 -0.2624689527931006E-01 5 3.00000 0.5138426125477819 5 4.00000 0.9355563118061758E-01 HERMITE_POLY_PHYS_VALUES_TEST: HERMITE_POLY_PHYS_VALUES returns values of the physicist's Hermite polynomials. N X H(N,X) 0 5.00000 1.000000000000000 1 5.00000 10.00000000000000 2 5.00000 98.00000000000000 3 5.00000 940.0000000000000 4 5.00000 8812.000000000000 5 5.00000 80600.00000000000 6 5.00000 717880.0000000000 7 5.00000 6211600.000000000 8 5.00000 52065680.00000000 9 5.00000 421271200.0000000 10 5.00000 3275529760.000000 11 5.00000 24329873600.00000 12 5.00000 171237081280.0000 5 0.00000 0.000000000000000 5 0.500000 41.00000000000000 5 1.00000 -8.000000000000000 5 3.00000 3816.000000000000 5 10.0000 3041200.000000000 HERMITE_POLY_PROB_VALUES_TEST: HERMITE_POLY_PROB_VALUES returns values of the probabilist's Hermite polynomials. N X He(N,X) 0 5.00000 1.000000000000000 1 5.00000 5.000000000000000 2 5.00000 24.00000000000000 3 5.00000 110.0000000000000 4 5.00000 478.0000000000000 5 5.00000 1950.000000000000 6 5.00000 7360.000000000000 7 5.00000 25100.00000000000 8 5.00000 73980.00000000000 9 5.00000 169100.0000000000 10 5.00000 179680.0000000000 11 5.00000 -792600.0000000000 12 5.00000 -5939480.000000000 5 0.00000 0.000000000000000 5 0.500000 6.281250000000000 5 1.00000 6.000000000000000 5 3.00000 18.00000000000000 5 10.0000 90150.00000000000 HYPER_1F1_VALUES_TEST: HYPER_1F1_VALUES returns values of the hypergeometric 1F1 function. A B X Hyper_1F1(A,B,X) -2.500000 3.300000 0.250000 0.818799 -0.500000 1.100000 0.250000 0.882840 0.500000 1.100000 0.250000 1.124502 2.500000 3.300000 0.250000 1.210105 -2.500000 3.300000 1.550000 0.127230 -0.500000 1.100000 1.550000 0.123260 0.500000 1.100000 1.550000 2.329795 2.500000 3.300000 1.550000 3.389002 -2.500000 3.300000 2.850000 -0.188195 -0.500000 1.100000 2.850000 -1.076420 0.500000 1.100000 2.850000 5.752182 2.500000 3.300000 2.850000 9.999857 0.825000 6.700000 0.250000 1.031721 1.100000 6.700000 0.250000 1.042487 1.650000 6.700000 0.250000 1.064311 3.300000 6.700000 0.250000 1.132184 0.825000 6.700000 1.550000 1.232840 1.100000 6.700000 1.550000 1.320065 1.650000 6.700000 1.550000 1.510481 3.300000 6.700000 1.550000 2.230752 0.825000 6.700000 2.850000 1.519729 1.100000 6.700000 2.850000 1.736494 1.650000 6.700000 2.850000 2.249233 3.300000 6.700000 2.850000 4.637774 HYPER_2F1_VALUES_TEST: HYPER_2F1_VALUES returns 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 1.086550409480700 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 0.5868208761512417E+19 1.100000 6.700000 -0.500000 0.850000 -446350101.4729600 1.100000 6.700000 0.500000 0.850000 5383505.756129573 3.300000 6.700000 4.500000 0.850000 20396.91377601966 hyper_2f1_complex_values_test(): hyper_2f1_complex_values returns values of the hypergeometric 2F1 function. A B C Z Hyper_2F1(A,B,C;Z) 3.200000 1.800000 6.700000 1.000000 0.000000 5.46900 0.00000 3.200000 -1.800000 6.700000 1.000000 0.000000 0.337506 0.00000 -5.000000 3.300000 6.700000 5.200000 4.800000 116.827 603.891 3.300000 -6.000000 3.700000 5.200000 -4.800000 17620.4 38293.8 -7.000000 3.300000 -3.700000 5.200000 -4.800000 -0.117728E+11 -0.143823E+11 4.300000 -8.000000 -3.700000 5.200000 4.800000 0.131612E+13 -0.101299E+12 3.300000 5.800000 6.700000 0.200000 0.100000 1.73306 0.634010 3.500000 -2.400000 6.700000 0.200000 0.500000 0.647622 -0.521105 3.300000 4.300000 6.700000 0.800000 0.300000 -1.48301 8.37443 7.000000 5.000000 4.100000 3.000000 -1.000000 -0.403761E-02 -0.295663E-02 5.000000 7.000000 4.100000 3.000000 -1.000000 -0.403761E-02 -0.295663E-02 3.500000 1.200000 9.700000 0.600000 0.900000 1.03431 0.544739 2.100000 5.400000 9.700000 0.500000 0.700000 0.688504 1.22742 8.700000 3.200000 6.700000 0.500000 0.700000 -0.900465 -1.11989 8.700000 2.700000 6.700000 0.600000 0.900000 -0.460839 -0.545757 hypergeometric_cdf_values_test: hypergeometric_cdf_values returns values of the Hypergeometric Cumulative Density Function. SAM SUC POP X HyperCDF(S,S,P)(X) 10 90 100 7 0.6001858177500578E-01 10 90 100 8 0.2615284665839845 10 90 100 9 0.6695237889132748 10 90 100 10 1.000000000000000 6 90 100 6 1.000000000000000 7 90 100 6 0.5332595856827856 8 90 100 6 0.1819495964117640 9 90 100 6 0.4448047017527730E-01 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 0.000000000000000 10 90 200 0 0.2088888139634505E-02 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 HYPERGEOMETRIC_PDF_VALUES_TEST: HYPERGEOMETRIC_PDF_VALUES returns values of the Hypergeometric Probability Density Function. SAM SUC POP X HyperPDF(S,S,P)(X) 10 90 100 7 0.5179370533242827E-01 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 0.3927689321042477E-01 10 10 100 6 0.3099828465518108E-04 10 30 100 6 0.3145116093938197E-01 10 50 100 6 0.2114132170316862 10 70 100 6 0.2075776621999210 10 90 90 0 0.000000000000000 10 90 200 0 0.2088888139634505E-02 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 HYPERGEOMETRIC_U_VALUES_TEST: HYPERGEOMETRIC_U_VALUES returns values of the hypergeometric U function. A B X HyperU(A,B,X) -2.500000 3.300000 0.250000 -68.69362872807861 -0.500000 1.100000 0.250000 -0.2971055137476107E-02 0.500000 1.100000 0.250000 1.500863174217780 2.500000 3.300000 0.250000 20.61468824420060 -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 0.2804640494187940 -2.500000 3.300000 2.850000 3.450815374144655 -0.500000 1.100000 2.850000 1.515663736875306 0.500000 1.100000 2.850000 0.5604211858793500 2.500000 3.300000 2.850000 0.6489714773513422E-01 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 returns values of the I0ML0 function. X F(X) 0.195312E-02 0.9987575551546175 0.156250E-01 0.9901135823070665 0.125000 0.9241943531002395 0.500000 0.7362426713471427 1.00000 0.5558226918141175 2.00000 0.3421515443446216 4.00000 0.1708717488877471 8.00000 0.8108100870921921E-01 12.0000 0.5344942144108958E-01 16.0000 0.3995032100892325E-01 16.2500 0.3933063743758492E-01 17.0000 0.3758227434280867E-01 20.0000 0.3191248655448039E-01 25.0000 0.2550614688350474E-01 30.0000 0.2124448031782529E-01 40.0000 0.1592549834855168E-01 50.0000 0.1273750692724259E-01 75.0000 0.8489775081478492E-02 100.000 0.6366834917845447E-02 125.000 0.5093284316312255E-02 I1ML1_VALUES_TEST: I1ML1_VALUES returns values of the I1ML1 function. X F(X) 0.195312E-02 0.9757534615538627E-03 0.156250E-01 0.7760929328060927E-02 0.125000 0.5930296640454537E-01 0.500000 0.2039521227673737 1.00000 0.3383947229366764 2.00000 0.4878770672696132 4.00000 0.5901873419657652 8.00000 0.6260453953031215 12.0000 0.6320931527490976 16.0000 0.6341017931323536 16.2500 0.6341796679757813 17.0000 0.6343926863239209 20.0000 0.6350157907325777 25.0000 0.6355961667735945 30.0000 0.6359100182669711 40.0000 0.6362211318175107 50.0000 0.6363648170213361 75.0000 0.6365065349961990 100.000 0.6365560912630026 125.000 0.6365790208718393 i4_fall_values_test(): i4_fall_values() returns some exact values of the 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_gpf_values_test(): i4_gpf_values() returns some exact values of the greatest prime factor function: N i4_gpf(N) 1 1 2 2 3 3 4 2 5 5 6 3 7 7 8 2 9 3 10 5 11 11 12 3 13 13 14 7 15 5 16 2 17 17 18 3 19 19 20 5 21 7 22 11 23 23 24 3 25 5 26 13 27 3 28 7 29 29 30 5 31 31 32 2 33 11 34 17 35 7 36 3 37 37 38 19 39 13 40 5 41 41 42 7 43 43 44 11 45 5 46 23 47 47 48 3 49 7 50 5 51 17 52 13 53 53 54 3 55 11 56 7 57 19 58 29 59 59 60 5 61 61 62 31 63 7 64 2 65 13 66 11 67 67 68 17 69 23 70 7 71 71 72 3 73 73 74 37 75 5 76 19 77 11 78 13 79 79 80 5 81 3 82 41 83 83 84 7 85 17 86 43 I4_RISE_VALUES_TEST: I4_RISE_VALUES returns some exact values of the 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 10 1 10 4000 1 4000 10 2 110 18 3 6840 4 4 840 98 3 970200 1 7 5040 INT_VALUES_TEST: INT_VALUES returns values of the INT function. X INT(X) -2.0100 -2.0000 -1.9900 -1.0000 -1.5000 -1.0000 -1.1000 -1.0000 -1.0100 -1.0000 -1.0000 -1.0000 -0.9900 0.0000 -0.9000 0.0000 -0.5100 0.0000 -0.5000 0.0000 -0.4900 0.0000 -0.0100 0.0000 0.0000 0.0000 0.0100 0.0000 0.4900 0.0000 0.5000 0.0000 0.5100 0.0000 0.9000 0.0000 0.9900 0.0000 1.0000 1.0000 1.0100 1.0000 1.1000 1.0000 1.5000 1.0000 1.9900 1.0000 2.0100 2.0000 INVERSE_CHI_SQUARE_PDF_VALUES_TEST: INVERSE_CHI_SQUARE_PDF_VALUES returns values of the inverse chi square Probability Density Function. DF X PDF 1.00000 0.100000 0.8500366602520341E-01 2.00000 0.100000 0.3368973499542734 1.00000 0.200000 0.3661245640481622 2.00000 0.200000 1.026062482798735 1.00000 0.400000 0.4518059816704532 2.00000 0.400000 0.8953274901880941 3.00000 0.400000 1.129514954176133 4.00000 0.400000 1.119159362735118 1.00000 1.00000 0.2419707245191433 2.00000 1.00000 0.3032653298563167 3.00000 1.00000 0.2419707245191433 4.00000 1.00000 0.1516326649281584 5.00000 1.00000 0.8065690817304778E-01 3.00000 2.00000 0.5492391118346530E-01 3.00000 3.00000 0.2166329508030457E-01 3.00000 4.00000 0.1100204146138436E-01 3.00000 5.00000 0.6457369034861447E-02 3.00000 6.00000 0.4162370481945731E-02 10.0000 1.00000 0.7897534631674914E-03 10.0000 2.00000 0.1584474249412852E-04 10.0000 3.00000 0.1511920090468204E-05 INVERSE_GAMMA_PDF_VALUES_TEST: INVERSE_GAMMA_PDF_VALUES returns values of the inverse gamma Probability Density Function. ALPHA BETA X PDF 1.00000 0.500000 1.00000 0.3032653298563167 1.00000 0.500000 2.00000 0.9735009788392561E-01 1.00000 0.500000 3.00000 0.4702676249392300E-01 1.00000 0.500000 4.00000 0.2757802820576861E-01 1.00000 2.00000 2.00000 0.1839397205857212 1.00000 3.00000 2.00000 0.1673476201113224 1.00000 4.00000 2.00000 0.1353352832366127 1.00000 5.00000 2.00000 0.1026062482798735 2.00000 2.00000 3.00000 0.7606179541223586E-01 3.00000 2.00000 3.00000 0.2535393180407862E-01 4.00000 2.00000 3.00000 0.5634207067573026E-02 5.00000 2.00000 3.00000 0.9390345112621711E-03 is_prime_values_test(): is_prime_values() returns values of the is_prime() function: n is_prime(n) 1 false 2 true 12 false 3 true 91 false 53 true 437 false 311 true 1333 false 719 true 16483 false 7919 true 223609 false 81799 true 873599 false 800573 true 5693761 false 7559173 true 90166053 false 69600977 true 6110601 false ******** true jacobi_cn_values_test: jacobi_cn_values_test() returns values of the Jacobi elliptic CN function. U M CN(U,M) 0.1000 0.000 0.9950041652780258 0.2000 0.000 0.9800665778412416 0.5000 0.000 0.8775825618903726 1.000 0.000 0.5403023058681397 2.000 0.000 -0.4161468365471424 0.1000 0.5000 0.9950124626090582 0.2000 0.5000 0.9801976276784098 0.5000 0.5000 0.8822663948904403 1.000 0.5000 0.5959765676721407 2.000 0.5000 -0.1031836155277618 0.1000 1.000 0.9950207489532265 0.2000 1.000 0.9803279976447253 0.5000 1.000 0.8868188839700739 1.000 1.000 0.6480542736638853 2.000 1.000 0.2658022288340797 4.000 1.000 0.3661899347368653E-01 -.2000 1.000 0.9803279976447253 -.5000 1.000 0.8868188839700739 -1.000 1.000 0.6480542736638853 -2.000 1.000 0.2658022288340797 jacobi_dn_values_test: jacobi_dn_values() returns values of the Jacobi elliptic DN function. U M DN(U,M) 0.1000 0.000 1.000000000000000 0.2000 0.000 1.000000000000000 0.5000 0.000 1.000000000000000 1.000 0.000 1.000000000000000 2.000 0.000 1.000000000000000 0.1000 0.5000 0.9975093485144243 0.2000 0.5000 0.9901483195224799 0.5000 0.5000 0.9429724257773857 1.000 0.5000 0.8231610016315963 2.000 0.5000 0.7108610477840873 0.1000 1.000 0.9950207489532265 0.2000 1.000 0.9803279976447253 0.5000 1.000 0.8868188839700739 1.000 1.000 0.6480542736638853 2.000 1.000 0.2658022288340797 4.000 1.000 0.3661899347368653E-01 -.2000 1.000 0.9803279976447253 -.5000 1.000 0.8868188839700739 -1.000 1.000 0.6480542736638853 -2.000 1.000 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 0.0000 1.0000 0.5000000000000000 1.000000000000000 1 0.0000 1.0000 0.5000000000000000 0.2500000000000000 2 0.0000 1.0000 0.5000000000000000 -0.3750000000000000 3 0.0000 1.0000 0.5000000000000000 -0.4843750000000000 4 0.0000 1.0000 0.5000000000000000 -0.1328125000000000 5 0.0000 1.0000 0.5000000000000000 0.2753906250000000 5 1.0000 1.0000 0.5000000000000000 -0.1640625000000000 5 2.0000 1.0000 0.5000000000000000 -1.174804687500000 5 3.0000 1.0000 0.5000000000000000 -2.361328125000000 5 4.0000 1.0000 0.5000000000000000 -2.616210937500000 5 5.0000 1.0000 0.5000000000000000 0.1171875000000000 5 0.0000 2.0000 0.5000000000000000 0.4218750000000000 5 0.0000 3.0000 0.5000000000000000 0.5048828125000000 5 0.0000 4.0000 0.5000000000000000 0.5097656250000000 5 0.0000 5.0000 0.5000000000000000 0.4306640625000000 5 0.0000 1.0000 -1.0000000000000000 -6.000000000000000 5 0.0000 1.0000 -0.8000000000000000 0.3862000000000000E-01 5 0.0000 1.0000 -0.6000000000000000 0.8118400000000000 5 0.0000 1.0000 -0.4000000000000000 0.3666000000000000E-01 5 0.0000 1.0000 -0.2000000000000000 -0.4851200000000000 5 0.0000 1.0000 0.0000000000000000 -0.3125000000000000 5 0.0000 1.0000 0.2000000000000000 0.1891200000000000 5 0.0000 1.0000 0.4000000000000000 0.4023400000000000 5 0.0000 1.0000 0.6000000000000000 0.1216000000000000E-01 5 0.0000 1.0000 0.8000000000000000 -0.4396200000000000 5 0.0000 1.0000 1.0000000000000000 1.000000000000000 jacobi_sn_values_test: jacobi_sn_values() returns values of the Jacobi elliptic SN function. U M SN(U,M) 0.1000 0.000 0.998334E-01 0.2000 0.000 0.198669 0.5000 0.000 0.479426 1.000 0.000 0.841471 2.000 0.000 0.909297 0.1000 0.5000 0.997507E-01 0.2000 0.5000 0.198022 0.5000 0.5000 0.470750 1.000 0.5000 0.803002 2.000 0.5000 0.994662 0.1000 1.000 0.996680E-01 0.2000 1.000 0.197375 0.5000 1.000 0.462117 1.000 1.000 0.761594 2.000 1.000 0.964028 4.000 1.000 0.999329 -.2000 1.000 -0.197375 -.5000 1.000 -0.462117 -1.000 1.000 -0.761594 -2.000 1.000 -0.964028 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 0.00 -4713 1 1 0.5000 1.00 -4713 1 2 0.5000 259261.00 -4004 10 26 0.5000 347998.50 -3761 10 8 0.0000 584282.50 -3114 9 6 0.0000 588465.75 -3102 2 18 0.2500 758325.50 -2637 3 8 0.0000 1438178.50 -776 7 9 0.0000 1446389.50 -753 1 1 0.0000 1448637.50 -747 2 26 0.0000 1448637.50 -747 2 26 0.0000 1607708.50 -312 9 1 0.0000 1607738.50 -312 10 1 0.0000 1713262.50 -23 8 29 0.0000 1721422.50 -1 12 31 0.0000 1721423.50 1 1 1 0.0000 1721425.50 1 1 3 0.0000 1721425.50 1 1 3 0.0000 1724220.50 8 8 29 0.0000 1741959.50 57 3 24 0.0000 1749994.50 79 3 24 0.0000 1825029.50 284 8 29 0.0000 1862836.50 388 3 3 0.0000 1922867.50 552 7 11 0.0000 1936747.50 590 7 12 0.0000 1940351.50 600 5 24 0.0000 1948320.50 622 3 19 0.0000 1948438.50 622 7 15 0.0000 1948439.50 622 7 16 0.0000 1952062.50 632 6 16 0.0000 1952067.50 632 6 21 0.0000 2114872.50 1078 3 17 0.0000 2289425.50 1556 2 9 0.0000 2299160.00 1582 10 4 0.5000 2299161.00 1582 10 15 0.5000 2333269.50 1676 3 4 0.0000 2361221.00 1752 9 13 0.5000 2361222.00 1752 9 14 0.5000 2372547.50 1783 9 18 0.0000 2375839.50 1792 9 22 0.0000 2394646.50 1844 3 21 0.0000 2394710.50 1844 5 24 0.0000 2400000.50 1858 11 17 0.0000 2415020.31 1899 12 31 0.8100 2440587.50 1970 1 1 0.0000 2444244.50 1980 1 6 0.0000 2450138.50 1996 2 25 0.0000 2451544.50 2000 1 1 0.0000 2453073.83 2004 3 9 0.3300 2456284.50 2012 12 23 0.0000 2913943.00 3266 1 1 0.5000 JED_MJD_VALUES_TEST: JED_MJD_VALUES returns: JED, a Julian Ephemeris Date, and MJD, the corresponding Modified Julian Day count. JED MJD 1507231.50 -892769.00 1660037.50 -739963.00 1746893.50 -653107.00 1770641.50 -629359.00 1892731.50 -507269.00 1931579.50 -468421.00 1974851.50 -425149.00 2091164.50 -308836.00 2121509.50 -278491.00 2155779.50 -244221.00 2174029.50 -225971.00 2191584.50 -208416.00 2195261.50 -204739.00 2229274.50 -170726.00 2245580.50 -154420.00 2266100.50 -133900.00 2288542.50 -111458.00 2290901.50 -109099.00 2323140.50 -76860.00 2334848.50 -65152.00 2348020.50 -51980.00 2366978.50 -33022.00 2385648.50 -14352.00 2392825.50 -7175.00 2416223.50 16223.00 2425848.50 25848.00 2430266.50 30266.00 2430833.50 30833.00 2431004.50 31004.00 2448698.50 48698.00 2450138.50 50138.00 2465737.50 65737.00 2486076.50 86076.00 JED_RD_VALUES_TEST: JED_RD_VALUES returns: JED, a Julian Ephemeris Date, and RD, the corresponding Reingold Dershowitz Day count. JED RD 1507231.50 -214193.00 1660037.50 -61387.00 1746893.50 25469.00 1770641.50 49217.00 1892731.50 171307.00 1931579.50 210155.00 1974851.50 253427.00 2091164.50 369740.00 2121509.50 400085.00 2155779.50 434355.00 2174029.50 452605.00 2191584.50 470160.00 2195261.50 473837.00 2229274.50 507850.00 2245580.50 524156.00 2266100.50 544676.00 2288542.50 567118.00 2290901.50 569477.00 2323140.50 601716.00 2334848.50 613424.00 2348020.50 626596.00 2366978.50 645554.00 2385648.50 664224.00 2392825.50 671401.00 2416223.50 694799.00 2425848.50 704424.00 2430266.50 708842.00 2430833.50 709409.00 2431004.50 709580.00 2448698.50 727274.00 2450138.50 728714.00 2465737.50 744313.00 2486076.50 764652.00 JED_WEEKDAY_VALUES_TEST: JED_WEEKDAY_VALUES returns Julian Ephemeris Dates (JED) and the corresponding weekday JED # Weekday 1507231.50 1 Sunday 1660037.50 4 Wednesday 1746893.50 4 Wednesday 1770641.50 1 Sunday 1892731.50 4 Wednesday 1931579.50 2 Monday 1974851.50 7 Saturday 2091164.50 1 Sunday 2121509.50 1 Sunday 2155779.50 6 Friday 2174029.50 7 Saturday 2191584.50 6 Friday 2195261.50 1 Sunday 2229274.50 1 Sunday 2245580.50 4 Wednesday 2266100.50 7 Saturday 2288542.50 7 Saturday 2290901.50 7 Saturday 2323140.50 4 Wednesday 2334848.50 1 Sunday 2348020.50 6 Friday 2366978.50 1 Sunday 2385648.50 2 Monday 2392825.50 4 Wednesday 2416223.50 1 Sunday 2425848.50 1 Sunday 2430266.50 2 Monday 2430833.50 2 Monday 2431004.50 5 Thursday 2448698.50 3 Tuesday 2450138.50 1 Sunday 2465737.50 4 Wednesday 2486076.50 1 Sunday KEI0_VALUES_TEST: KEI0_VALUES returns values of the Kelvin function KEI of order 0 X KEI0 0.00000 0.000000000000000 0.500000 -0.6715816950943676 1.00000 -0.4949946365187199 1.50000 -0.3313955623385585 2.00000 -0.2024000677647043 2.50000 -0.1106960991556749 3.00000 -0.5112188404598678E-01 3.50000 -0.1600256851827124E-01 4.00000 0.2198399294972520E-02 4.50000 0.9720918540151989E-02 5.00000 0.1118758650986964E-01 KEI1_VALUES_TEST: KEI1_VALUES returns values of the Kelvin function KEI of order 1 X KEI1 0.500000 -1.051182085412523 1.00000 -0.2419959664297382 1.50000 0.1008680985009855E-02 2.00000 0.8004939780706674E-01 2.50000 0.9331378813535750E-01 3.00000 0.8027022252392219E-01 3.50000 0.5937625647622691E-01 4.00000 0.3916601076917133E-01 4.50000 0.2300216024690250E-01 5.00000 0.1157775439325247E-01 KER0_VALUES_TEST: KER0_VALUES returns values of the Kelvin function KER of order 0 X KER0 0.500000 0.8559058721186342 1.00000 0.2867062087283160 1.50000 0.5293491548771044E-01 2.00000 -0.4166451399150953E-01 2.50000 -0.6968797258904534E-01 3.00000 -0.6702923330379870E-01 3.50000 -0.5263927724224119E-01 4.00000 -0.3617884789954761E-01 4.50000 -0.2199987504667382E-01 5.00000 -0.1151172719949066E-01 KER1_VALUES_TEST: KER1_VALUES returns values of the Kelvin function KER of order 1 X KER1 0.500000 -1.522403406532090 1.00000 -0.7403222768419827 1.50000 -0.4170442851662574 2.00000 -0.2308059295181230 2.50000 -0.1172561358598705 3.00000 -0.4989830778751491E-01 3.50000 -0.1272324936181659E-01 4.00000 0.5351296460277448E-02 4.50000 0.1209090413515866E-01 5.00000 0.1273739048421857E-01 LAGUERRE_ASSOCIATED_VALUES_TEST: LAGUERRE_ASSOCIATED_VALUES returns values of the associated Laguerre polynomials. N M X L(N,M)(X) 1 0 0.00000 1.000000000000000 2 0 0.00000 1.000000000000000 3 0 0.00000 1.000000000000000 4 0 0.00000 1.000000000000000 5 0 0.00000 1.000000000000000 1 1 0.500000 1.500000000000000 2 1 0.500000 1.625000000000000 3 1 0.500000 1.479166666666667 4 1 0.500000 1.148437500000000 3 0 0.200000 0.4586666666666667 3 1 0.200000 2.878666666666667 3 2 0.200000 8.098666666666666 3 3 0.200000 17.11866666666667 4 2 0.250000 10.45328776041667 5 2 0.250000 13.29019368489583 6 3 0.250000 56.22453647189670 7 3 0.250000 74.84729341779436 8 4 0.250000 323.8912982762806 9 4 0.250000 442.6100000097533 10 5 0.250000 1936.876572288250 LAGUERRE_GENERAL_VALUES_TEST: LAGUERRE_GENERAL_VALUES returns values of the generalized Laguerre function. N A X L(N,A)(X) 5 0.00000 0.250000 0.3726399739583333E-01 5 0.250000 0.250000 0.3494791666666667 5 0.500000 0.250000 0.8710042317708333 5 0.750000 0.250000 1.672395833333333 5 1.50000 0.250000 6.657625325520833 5 2.50000 0.250000 23.95726725260417 5 5.00000 0.250000 203.1344319661458 8 1.20000 0.00000 12.84193996800000 8 1.20000 0.200000 5.359924801587302 8 1.20000 0.400000 0.9204589064126985 8 1.20000 0.600000 -1.341585114857143 8 1.20000 0.800000 -2.119726307555556 8 1.20000 1.00000 -1.959193658349206 0 5.20000 0.750000 1.000000000000000 1 5.20000 0.750000 5.450000000000000 2 5.20000 0.750000 17.20125000000000 3 5.20000 0.750000 41.10393750000000 4 5.20000 0.750000 82.39745859375000 5 5.20000 0.750000 146.0179186171875 6 5.20000 0.750000 235.9204608298828 LAGUERRE_POLYNOMIAL_VALUES_TEST: LAGUERRE_POLYNOMIAL_VALUES returns values of the Laguerre polynomials. N X L(N)(X) 0 1.00000 1.000000000000000 1 1.00000 0.000000000000000 2 1.00000 -0.5000000000000000 3 1.00000 -0.6666666666666667 4 1.00000 -0.6250000000000000 5 1.00000 -0.4666666666666667 6 1.00000 -0.2569444444444444 7 1.00000 -0.4047619047619048E-01 8 1.00000 0.1539930555555556 9 1.00000 0.3097442680776014 10 1.00000 0.4189459325396825 11 1.00000 0.4801341790925124 12 1.00000 0.4962122235082305 5 0.500000 -0.4455729166666667 5 3.00000 0.8500000000000000 5 5.00000 -3.166666666666667 5 10.0000 34.33333333333333 lambert_w_values_test(): lambert_w_values() returns values of the Lambert W function. X Branch W(X) -0.367879E-01 -1 -4.889720169867429 -0.735759E-01 -1 -3.994308347002122 -0.110364 -1 -3.439216483280204 -0.147152 -1 -3.022313245324657 -0.183940 -1 -2.678346990016661 -0.220728 -1 -2.376421342062887 -0.257516 -1 -2.097349210703492 -0.294304 -1 -1.824388309032984 -0.331091 -1 -1.531811608389612 -0.367879 -1 -1.000000000000000 -0.331091 0 -0.6083412847334320 -0.294304 0 -0.4716719097435220 -0.257516 0 -0.3744931340194980 -0.220728 0 -0.2970834624464240 -0.183940 0 -0.2319609529865340 -0.147152 0 -0.1753565005292990 -0.110364 0 -0.1250669829825240 -0.735759E-01 0 -0.7967816051147700E-01 -0.367879E-01 0 -0.3822124174679900E-01 0.00000 0 0.000000000000000 0.500000 0 0.3517337112491958 1.00000 0 0.5671432904097840 1.50000 0 0.7258613577662263 2.00000 0 0.8526055020137255 2.50000 0 0.9585863567287028 2.71828 0 1.000000000000000 3.00000 0 1.049908894964040 3.50000 0 1.130289326974136 4.00000 0 1.202167873197043 4.50000 0 1.267237814307435 5.00000 0 1.326724665242200 5.50000 0 1.381545379445041 6.00000 0 1.432404775898300 6.50000 0 1.479856830173851 7.00000 0 1.524345204984144 7.50000 0 1.566230953782388 8.00000 0 1.605811996320178 10.0000 0 1.745528002740699 100.000 0 3.385630140290050 1000.00 0 5.249602852401596 0.100000E+07 0 11.38335808614005 LAPLACE_CDF_VALUES_TEST: LAPLACE_CDF_VALUES returns values of the Laplace CDF. MU BETA X CDF(MU,BETA,X) 0.00000 1.00000 0.00000 0.5000000000000000 0.00000 1.00000 1.00000 0.8160602794142788 0.00000 1.00000 2.00000 0.9323323583816937 0.00000 1.00000 3.00000 0.9751064658160680 0.00000 2.00000 1.00000 0.6967346701436833 0.00000 3.00000 1.00000 0.6417343447131054 0.00000 4.00000 1.00000 0.6105996084642976 0.00000 5.00000 1.00000 0.5906346234610091 1.00000 2.00000 1.00000 0.5000000000000000 2.00000 2.00000 1.00000 0.3032653298563167 3.00000 2.00000 1.00000 0.1839397205857212 4.00000 2.00000 1.00000 0.1115650800742149 LEGENDRE_ASSOCIATED_VALUES_TEST: LEGENDRE_ASSOCIATED_VALUES returns values of the associated Legendre polynomials. N M X P(N,M)(X) 1 0 0.00000 0.000000000000000 2 0 0.00000 -0.5000000000000000 3 0 0.00000 0.000000000000000 4 0 0.00000 0.3750000000000000 5 0 0.00000 0.000000000000000 1 1 0.500000 -0.8660254037844386 2 1 0.500000 -1.299038105676658 3 1 0.500000 -0.3247595264191645 4 1 0.500000 1.353164693413185 3 0 0.200000 -0.2800000000000000 3 1 0.200000 1.175755076535925 3 2 0.200000 2.880000000000000 3 3 0.200000 -14.10906091843111 4 2 0.250000 -3.955078125000000 5 2 0.250000 -9.997558593750000 6 3 0.250000 82.65311444100485 7 3 0.250000 20.24442836815152 8 4 0.250000 -423.7997531890869 9 4 0.250000 1638.320624828339 10 5 0.250000 -20256.87389227225 LEGENDRE_ASSOCIATED_NORMALIZED_VALUES_TEST: LEGENDRE_ASSOCIATED_NORMALIZED_VALUES returns 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 -1.018924927466445 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 1.034723155272289 5 5 0.500000 -0.5667412129155530 LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES_TEST: LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES returns 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 -0.7884789131313000E-01 2 1 0.500000 -0.3345232717786446 2 2 0.500000 0.2897056515173922 3 0 0.500000 -0.3265292910163510 3 1 0.500000 -0.6997056236064664E-01 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 0.8405804426339820E-01 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 returns values of the Legendre QN polynomials. N X Q(N)(X) 0 0.250000 0.255413 1 0.250000 -0.936147 2 0.250000 -0.478761 3 0.250000 0.424614 4 0.250000 0.544840 5 0.250000 -0.945133E-01 6 0.250000 -0.497352 7 0.250000 -0.149902 8 0.250000 0.364916 9 0.250000 0.305568 10 0.250000 -0.183280 3 0.00000 0.666667 3 0.100000 0.626867 3 0.200000 0.509902 3 0.300000 0.323275 3 0.400000 0.802611E-01 3 0.500000 -0.198655 3 0.600000 -0.482866 3 0.700000 -0.725289 3 0.800000 -0.845444 3 0.900000 -0.662710 LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES_TEST: LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES returns values of the normalized Legendre polynomials. N X Pn(N)(X) 0 0.250000 0.7071067811865475 1 0.250000 0.3061862178478972 2 0.250000 -0.6423376497217020 3 0.250000 -0.6284815141846855 4 0.250000 0.3345637065282053 5 0.250000 0.7967179601799685 6 0.250000 0.6189376866246124E-01 7 0.250000 -0.7665888509210890 8 0.250000 -0.4444760242953344 9 0.250000 0.5450094674858101 10 0.250000 0.7167706229835538 3 0.00000 0.000000000000000 3 0.100000 -0.2759472322745781 3 0.200000 -0.5238320341483518 3 0.300000 -0.7155919752205163 3 0.400000 -0.8231646250902670 3 0.500000 -0.8184875533567997 3 0.600000 -0.6734983296193094 3 0.700000 -0.3601345234769920 3 0.800000 0.1496662954709581 3 0.900000 0.8839665576253438 3 1.00000 1.870828693386971 LEGENDRE_POLYNOMIAL_VALUES_TEST: LEGENDRE_POLYNOMIAL_VALUES returns values of the Legendre PN polynomials. N X P(N)(X) 0 0.250000 1.000000000000000 1 0.250000 0.2500000000000000 2 0.250000 -0.4062500000000000 3 0.250000 -0.3359375000000000 4 0.250000 0.1577148437500000 5 0.250000 0.3397216796875000 6 0.250000 0.2427673339843750E-01 7 0.250000 -0.2799186706542969 8 0.250000 -0.1524540185928345 9 0.250000 0.1768244206905365 10 0.250000 0.2212002165615559 3 0.00000 0.000000000000000 3 0.100000 -0.1475000000000000 3 0.200000 -0.2800000000000000 3 0.300000 -0.3825000000000000 3 0.400000 -0.4400000000000000 3 0.500000 -0.4375000000000000 3 0.600000 -0.3600000000000000 3 0.700000 -0.1925000000000000 3 0.800000 0.8000000000000000E-01 3 0.900000 0.4725000000000000 3 1.00000 1.000000000000000 LEGENDRE_SHIFTED_POLYNOMIAL_VALUES_TEST: LEGENDRE_SHIFTED_POLYNOMIAL_VALUES returns values of the shifted Legendre PN polynomials. N X P(N)(X) 0 0.625000 1.000000000000000 1 0.625000 0.2500000000000000 2 0.625000 -0.4062500000000000 3 0.625000 -0.3359375000000000 4 0.625000 0.1577148437500000 5 0.625000 0.3397216796875000 6 0.625000 0.2427673339843750E-01 7 0.625000 -0.2799186706542969 8 0.625000 -0.1524540185928345 9 0.625000 0.1768244206905365 10 0.625000 0.2212002165615559 3 0.500000 0.000000000000000 3 0.550000 -0.1475000000000000 3 0.600000 -0.2800000000000000 3 0.650000 -0.3825000000000000 3 0.700000 -0.4400000000000000 3 0.750000 -0.4375000000000000 3 0.800000 -0.3600000000000000 3 0.850000 -0.1925000000000000 3 0.900000 0.8000000000000000E-01 3 0.950000 0.4725000000000000 3 1.00000 1.000000000000000 LERCH_VALUES_TEST: LERCH_VALUES returns values of the Lerch transcendent function. Z S A CDF 1.000 2 0.000 1.644934066848226 1.000 3 0.000 1.202056903159594 1.000 10 0.000 1.000994575127818 0.5000 2 1.000 1.164481052930025 0.5000 3 1.000 1.074426387216080 0.5000 10 1.000 1.000492641212014 0.3333 2 2.000 0.2959190697935714 0.3333 3 2.000 0.1394507503935608 0.3333 10 2.000 0.9823175058446061E-03 0.1000 2 3.000 0.1177910993911311 0.1000 3 3.000 0.3868447922298962E-01 0.1000 10 3.000 0.1703149614186634E-04 LOBACHEVSKY_VALUES_TEST: LOBACHEVSKY_VALUES returns values of the Lobachevsky function. X F(X) 0.195312E-02 0.1241763906516139E-08 0.781250E-02 0.7947334477000109E-07 0.312500E-01 0.5086759818620883E-05 0.125000 0.3260309790120720E-03 0.500000 0.2138053681540822E-01 1.00000 0.1875381690208383 1.50000 0.8305119997188365 2.00000 1.885436242667903 2.50000 2.131598898651641 3.00000 2.177112018561343 4.00000 2.292102792189665 5.00000 3.913719502878449 6.00000 4.351356398383643 7.00000 4.420064496847819 10.0000 6.565601313362383 15.0000 10.82550466150460 20.0000 13.36551285547423 30.0000 21.13100268563996 50.0000 34.83823658944912 100.000 69.65706243783740 lobatto_polynomial_values_test(): lobatto_polynomial_values() returns values of the complete 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 -1.501464843750000 5 0.250000 0.3639221191406250 6 0.250000 2.001914978027344 7 0.250000 0.6597948074340820 8 0.250000 -1.934441328048706 9 0.250000 -1.769941113889217 10 0.250000 1.215243665501475 3 -1.00000 0.000000000000000 3 -0.900000 0.8692500000000000 3 -0.800000 1.188000000000000 3 -0.700000 1.109250000000000 3 -0.600000 0.7680000000000000 3 -0.500000 0.2812500000000000 3 -0.400000 -0.2520000000000000 3 -0.300000 -0.7507500000000000 3 -0.200000 -1.152000000000000 3 -0.100000 -1.410750000000000 3 0.00000 -1.500000000000000 3 0.100000 -1.410750000000000 3 0.200000 -1.152000000000000 3 0.300000 -0.7507500000000000 3 0.400000 -0.2520000000000000 3 0.500000 0.2812500000000000 3 0.600000 0.7680000000000000 3 0.700000 1.109250000000000 3 0.800000 1.188000000000000 3 0.900000 0.8692500000000000 3 1.00000 0.000000000000000 lobatto_polynomial_derivative_values_test(): lobatto_polynomial_derivative_values() returns derivatives of the complete Lobatto polynomials. N X Lo'(N)(X) 1 0.250000 -0.5000000000000000 2 0.250000 2.437500000000000 3 0.250000 4.031250000000000 4 0.250000 -3.154296875000000 5 0.250000 -10.19165039062500 6 0.250000 -1.019622802734375 7 0.250000 15.67544555664063 8 0.250000 10.97668933868408 9 0.250000 -15.91419786214828 10 0.250000 -24.33202382177114 3 -1.00000 12.00000000000000 3 -0.900000 5.670000000000000 3 -0.800000 0.9600000000000000 3 -0.700000 -2.310000000000000 3 -0.600000 -4.320000000000000 3 -0.500000 -5.250000000000000 3 -0.400000 -5.280000000000000 3 -0.300000 -4.590000000000000 3 -0.200000 -3.360000000000000 3 -0.100000 -1.770000000000000 3 0.00000 0.000000000000000 3 0.100000 1.770000000000000 3 0.200000 3.360000000000000 3 0.300000 4.590000000000000 3 0.400000 5.280000000000000 3 0.500000 5.250000000000000 3 0.600000 4.320000000000000 3 0.700000 2.310000000000000 3 0.800000 -0.9600000000000000 3 0.900000 -5.670000000000000 3 1.00000 -12.00000000000000 LOG_VALUES_TEST: LOG_VALUES returns values of the natural logarithm function. X LN(X) 0.100000E-04 -11.51292546497023 0.100000E-01 -4.605170185988092 0.100000 -2.302585092994046 0.200000 -1.609437912434100 0.300000 -1.203972804325936 0.400000 -0.9162907318741551 0.500000 -0.6931471805599453 0.600000 -0.5108256237659907 0.700000 -0.3566749439387324 0.800000 -0.2231435513142098 0.900000 -0.1053605156578263 1.00000 0.000000000000000 2.00000 0.6931471805599453 3.00000 1.098612288668110 3.14159 1.144729885849400 5.00000 1.609437912434100 10.0000 2.302585092994046 20.0000 2.995732273553991 100.000 4.605170185988092 0.123457E+09 18.63140176616802 LOG_NORMAL_CDF_VALUES_TEST: LOG_NORMAL_CDF_VALUES returns values of the Log Normal Cumulative Density Function. MU SIGMA X CDF 1.00000 0.500000 1.00000 0.2275013194817921E-01 1.00000 0.500000 2.00000 0.2697049307349095 1.00000 0.500000 3.00000 0.5781741008028732 1.00000 0.500000 4.00000 0.7801170895122241 1.00000 2.00000 2.00000 0.4390310097476894 1.00000 3.00000 2.00000 0.4592655190218048 1.00000 4.00000 2.00000 0.4694258497695908 1.00000 5.00000 2.00000 0.4755320473858733 2.00000 2.00000 3.00000 0.3261051056816658 3.00000 2.00000 3.00000 0.1708799040927608 4.00000 2.00000 3.00000 0.7343256357952060E-01 5.00000 2.00000 3.00000 0.2554673736161761E-01 LOG_SERIES_CDF_VALUES_TEST: LOG_SERIES_CDF_VALUES returns values of the Log Series Cumulative Density Function. T N CDF 0.1000 1 0.9491221581029903 0.1111 1 0.9433541128559735 0.1250 1 0.9361094611773272 0.1429 1 0.9267370278044118 0.1667 1 0.9141358246245129 0.2000 1 0.8962840235449100 0.2500 1 0.8690148741955517 0.3333 1 0.8221011541254772 0.5000 1 0.7213475204444817 0.6667 1 0.6068261510845583 0.7500 1 0.5410106403333613 0.8000 1 0.4970679476476894 0.8333 1 0.4650921887927060 0.8571 1 0.4404842934597863 0.8750 1 0.4207860535926143 0.8889 1 0.4045507673897055 0.9000 1 0.3908650337129266 0.9900 1 0.2149757685421097 0.9900 0 0.000000000000000 0.9900 1 0.2149757685421097 0.9900 2 0.3213887739704539 0.9900 3 0.3916213575531612 0.9900 4 0.4437690508633213 0.9900 5 0.4850700239649681 0.9900 6 0.5191433267738267 0.9900 7 0.5480569580144867 0.9900 8 0.5731033910767085 0.9900 9 0.5951442521714636 0.9900 10 0.6147826594068904 LOG10_VALUES_TEST: LOG10_VALUES returns values of the logarithm base 10 function. X LOG10(X) 0.100000E-04 -5.000000000000000 0.100000E-01 -2.000000000000000 0.100000 -1.000000000000000 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 -0.9691001300805642E-01 0.900000 -0.4575749056067512E-01 1.00000 0.000000000000000 2.00000 0.3010299956639812 3.00000 0.4771212547196624 3.14159 0.4971498726941339 5.00000 0.6989700043360189 10.0000 1.000000000000000 20.0000 1.301029995663981 100.000 2.000000000000000 0.123457E+09 8.091514977169270 LOGARITHMIC_INTEGRAL_VALUES_TEST: LOGARITHMIC_INTEGAL_VALUES returns values of the logarithmic integral function. X LI(X) 0.00000 0.000000000000000 0.100000 -0.3238978959329102E-01 0.200000 -0.8512648672879405E-01 0.300000 -0.1574149028946895 0.400000 -0.2529494192126213 0.500000 -0.3786710430610880 0.600000 -0.5468514142104171 0.700000 -0.7809468775455607 0.800000 -1.134011957382327 0.900000 -1.775800683423525 0.950000 -2.443622553873225 0.975000 -3.124190050507211 1.03125 -2.872935510329120 1.06250 -2.164282524138207 1.12500 -1.440351296279408 1.25000 -0.6864884538258716 1.50000 0.1250649863152964 2.00000 1.045163780117493 4.00000 2.967585095039051 8.00000 5.253718299558931 16.0000 8.519716463711060 32.0000 13.60509217709172 64.0000 21.93466832805100 128.000 36.04254831722944 256.000 60.51306533791733 512.000 103.7211171690373 1024.00 181.0780396816945 2048.00 321.1144156746837 LOGISTIC_CDF_VALUES_TEST: LOGISTIC_CDF_VALUES returns values of the Logistic Cumulative Density Function. MU BETA X CDF 1.00000 0.500000 1.00000 0.5000000000000000 1.00000 0.500000 2.00000 0.8807970779778824 1.00000 0.500000 3.00000 0.9820137900379085 1.00000 0.500000 4.00000 0.9975273768433652 1.00000 2.00000 2.00000 0.6224593312018546 1.00000 3.00000 2.00000 0.5825702064623147 1.00000 4.00000 2.00000 0.5621765008857981 1.00000 5.00000 2.00000 0.5498339973124780 2.00000 2.00000 3.00000 0.6224593312018546 3.00000 2.00000 3.00000 0.5000000000000000 4.00000 2.00000 3.00000 0.3775406687981454 5.00000 2.00000 3.00000 0.2689414213699951 MATHIEU_EVEN_VALUES_TEST: MATHIEU_EVEN_VALUES returns values of the eigenvalues of the Mathieu differential equation associated with even periodic solutions. R Q A(R,Q) 0 0 0.00000 1 0 1.00000 2 0 4.00000 15 0 225.000 5 0 25.0000 5 5 25.5500 5 10 27.7038 5 15 31.9578 5 20 36.6450 5 25 40.0502 0 5 -5.80005 0 25 -40.2568 1 20 -14.4913 2 15 5.07798 10 10 100.507 MATHIEU_ODD_VALUES_TEST: MATHIEU_ODD_VALUES returns values of the eigenvalues of the Mathieu differential equation associated with odd periodic solutions. R Q B(R,Q) 1 0 1.00000 1 25 -40.2568 2 0 4.00000 2 5 2.09946 2 10 -2.38216 2 15 -8.09935 2 20 -14.4911 2 25 -21.3149 5 15 27.9679 10 0 100.000 10 10 100.507 15 0 225.000 15 20 225.895 mcnugget_number_values_test():: mcnugget_number_values() returns values of the McNugget numbers. N M(N) 0 1 1 0 2 0 3 0 4 0 5 0 6 1 7 0 8 0 9 1 10 0 11 0 12 1 13 0 14 0 15 1 16 0 17 0 18 2 19 0 20 1 21 1 22 0 23 0 24 2 25 0 26 1 27 2 28 0 29 1 30 2 31 0 32 1 33 2 34 0 35 1 36 3 37 0 38 2 39 2 40 1 41 1 42 3 43 0 44 2 45 3 46 1 47 2 48 3 49 1 50 2 51 3 52 1 53 2 54 4 55 1 56 3 57 3 58 2 59 2 60 5 61 1 62 3 63 4 64 2 65 3 66 5 67 2 68 3 69 5 70 2 71 3 72 6 73 2 74 4 75 5 76 3 77 3 78 7 79 2 80 5 81 6 82 3 83 4 84 7 85 3 86 5 87 7 88 3 89 5 90 8 91 3 92 6 93 7 94 4 95 5 96 9 97 3 98 7 99 8 100 5 mersenne_prime_values_test(): mersenne_prime_values() returns indices of Mersenne primes. n mersenne_prime(n) 1 2 2 3 3 5 4 7 5 13 6 17 7 19 8 31 9 61 10 89 11 107 12 127 13 521 14 607 15 1279 16 2203 17 2281 18 3217 19 4253 20 4423 21 9689 22 9941 23 11213 24 19937 25 21701 26 23209 27 44497 28 86243 29 110503 30 132049 31 216091 32 756839 33 859433 34 1257787 35 1398269 36 2976221 37 3021377 38 6972593 39 13466917 40 20996011 41 24036583 42 25964951 43 30402457 44 32582657 45 37156667 46 42643801 47 43112609 48 57885161 49 74207281 50 77232917 51 82589933 mertens_values_test(): 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 returns values of the one-parameter Mittag-Leffler function E(A;X). A X E(A;X) 0.2500 0.0000 1.000000000000000 0.2500 -2.5000 0.2525646348870172 0.2500 -5.0000 0.1427989464258737 0.2500 -7.5000 0.9942310913929360E-01 0.2500 -10.0000 0.7623703523972160E-01 1.7500 0.0000 1.000000000000000 1.7500 -12.5000 -0.2579027070618285 1.7500 -25.0000 0.2716853059670252 1.7500 -37.5000 0.1846579916604009E-01 1.7500 -50.0000 -0.1397073896421940 2.2500 0.0000 1.000000000000000 2.2500 -25.0000 -1.022121843823497 2.2500 -50.0000 1.860844522589611 2.2500 -75.0000 2.644615445996891 2.2500 -100.0000 0.7762512036620307 1.0000 -5.0000 0.6737946999045729E-02 2.0000 -5.0000 -0.6172728764571668 3.0000 -5.0000 0.2010457248089053 4.0000 -5.0000 0.7922864454196143 5.0000 -5.0000 0.9583402225672250 6.0000 -5.0000 0.9930556077474290 7.0000 -5.0000 0.9990079367947130 8.0000 -5.0000 0.9998759920646870 9.0000 -5.0000 0.9999862213403840 10.0000 -5.0000 0.9999986221340380 MITTAG_LEFFLER_EAB_VALUES_TEST: MITTAG_LEFFLER_EAB_VALUES returns values of the two-parameter Mittag-Leffler function E(A;X). A B X EB(A;B,X) 1.0000 0.0000 -0.2500 -0.1947001957678512 1.0000 2.5000 -0.2500 0.6821152851737027 1.0000 5.0000 -0.2500 0.3966713294631294E-01 1.5000 0.0000 -1.2500 -0.7783327874361643 1.5000 5.0000 -1.2500 0.3761895766689720E-01 1.5000 10.0000 -1.2500 0.2653864659692168E-05 3.0000 1.0000 -2.7500 0.5521129475536116 3.0000 1.1000 -2.7500 0.6561318862220054 3.0000 1.2000 -2.7500 0.7417555514147703 1.5000 5.0000 -5.0000 0.2836279996533230E-01 1.5000 10.0000 -5.0000 0.2382766080122566E-05 1.5000 15.0000 -5.0000 0.1057337628882522E-10 1.5000 5.0000 5.0000 0.6524069073077504E-01 2.0000 5.0000 5.0000 0.4926693884523065E-01 2.5000 5.0000 5.0000 0.4440848516337653E-01 2.0000 1.0000 2.0000 2.178183556608570 2.0000 2.0000 2.0000 1.368298872008591 2.0000 3.0000 2.0000 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 0.441000 1 0.7000 2 2 0.3000 2 4 2 0.264600 1 0.5000 2 2 0.5000 1 3 2 0.375000 1 0.6000 1 2 0.0000 1 3 0.4000 1 3 3 0.00000 1 0.6000 3 2 0.1000 0 3 0.1000 0 4 0.1000 0 5 0.1000 0 3 5 0.216000 1 0.6000 2 2 0.1000 1 3 0.1000 0 4 0.1000 0 5 0.1000 0 3 5 0.108000 1 0.6000 1 2 0.1000 0 3 0.1000 2 4 0.1000 0 5 0.1000 0 3 5 0.180000E-01 1 0.6000 1 2 0.1000 0 3 0.1000 0 4 0.1000 1 5 0.1000 1 3 5 0.360000E-01 1 0.6000 0 2 0.1000 0 3 0.1000 0 4 0.1000 3 5 0.1000 0 3 5 0.100000E-02 1 0.6000 0 2 0.1000 1 3 0.1000 1 4 0.1000 1 5 0.1000 0 3 5 0.600000E-02 NEGATIVE_BINOMIAL_CDF_VALUES_TEST: NEGATIVE_BINOMIAL_CDF_VALUES returns values of the Negative Binomial Cumulative Density Function. F S P CDF 4 4 0.500000 0.636719 3 5 0.500000 0.363281 2 6 0.500000 0.144531 3 4 0.500000 0.500000 2 5 0.500000 0.226562 1 6 0.500000 0.625000E-01 2 4 0.500000 0.343750 1 5 0.500000 0.109375 0 6 0.500000 0.156250E-01 2 4 0.400000 0.179200 1 5 0.400000 0.409600E-01 0 6 0.400000 0.409600E-02 2 4 0.300000 0.704700E-01 1 5 0.300000 0.109350E-01 0 6 0.300000 0.729000E-03 11 1 0.300000 0.986159 10 2 0.300000 0.914975 9 3 0.300000 0.747185 17 1 0.100000 0.849905 16 2 0.100000 0.549716 15 3 0.100000 0.266204 9 1 0.100000 0.651322 8 2 0.100000 0.263901 7 3 0.100000 0.701908E-01 2 0 0.100000E-01 1.00000 1 1 0.100000E-01 0.199000E-01 0 2 0.100000E-01 0.100000E-03 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 0.4270039294528318E-03 1.50 8.00 7.00 6.50 7.50 7.50 6.00 10.00 6.00 -0.1228915451058514E-02 2.00 8.00 7.00 6.50 7.50 7.50 6.00 10.00 6.00 -0.1944260688400887E-03 1.00 3.00 2.00 4.00 1.50 3.00 3.50 2.00 2.00 0.3338419923885592E-02 1.50 3.00 2.00 4.00 1.50 3.00 3.50 2.00 2.00 -0.7958936865080434E-03 2.00 3.00 2.00 4.00 1.50 3.00 3.50 2.00 2.00 -0.4338208690251972E-02 0.50 0.50 1.00 2.00 1.00 1.50 1.50 0.50 1.50 0.5379143536399187E-01 1.00 0.50 1.00 2.00 1.00 1.50 1.50 0.50 1.50 0.6211299937499411E-02 1.50 0.50 1.00 2.00 1.00 1.50 1.50 0.50 1.50 0.3042903097250921E-01 NORMAL_01_CDF_VALUES_TEST: NORMAL_01_CDF_VALUES returns values of the Normal Cumulative Density Function. X CDF 0.00000 0.5000000000000000 0.100000 0.5398278372770290 0.200000 0.5792597094391030 0.300000 0.6179114221889526 0.400000 0.6554217416103242 0.500000 0.6914624612740131 0.600000 0.7257468822499270 0.700000 0.7580363477769270 0.800000 0.7881446014166033 0.900000 0.8159398746532405 1.00000 0.8413447460685429 1.50000 0.9331927987311419 2.00000 0.9772498680518208 2.50000 0.9937903346742240 3.00000 0.9986501019683699 3.50000 0.9997673709209645 4.00000 0.9999683287581669 NORMAL_01_PDF_VALUES_TEST: NORMAL_01_PDF_VALUES returns values of the Normal Probability Density Function. X PDF -2.25265 0.3155059887555709E-01 3.65054 0.5094586261557538E-03 2.63607 0.1235886992552887E-01 0.493564 0.3531928626012750 -0.677543 0.3171212685764107 -3.47105 0.9653372813755943E-03 -1.93938 0.6083856556197816E-01 -3.12035 0.3066504313116445E-02 -3.64937 0.5116437388114821E-03 1.07173 0.2246444116615346 NORMAL_CDF_VALUES_TEST: NORMAL_CDF_VALUES returns values of the Normal Cumulative Density Function. MU SIGMA X CDF 1.00000 0.500000 1.00000 0.5000000000000000 1.00000 0.500000 2.00000 0.9772498680518208 1.00000 0.500000 3.00000 0.9999683287581669 1.00000 0.500000 4.00000 0.9999999990134124 1.00000 2.00000 2.00000 0.6914624612740131 1.00000 3.00000 2.00000 0.6305586598182364 1.00000 4.00000 2.00000 0.5987063256829237 1.00000 5.00000 2.00000 0.5792597094391030 2.00000 2.00000 3.00000 0.6914624612740131 3.00000 2.00000 3.00000 0.5000000000000000 4.00000 2.00000 3.00000 0.3085375387259869 5.00000 2.00000 3.00000 0.1586552539314571 NORMAL_PDF_VALUES_TEST: NORMAL_PDF_VALUES returns values of the Normal Probability Density Function. MU SIGMA X PDF -56.3163 4.78596 -46.8542 0.1180775937213258E-01 12.3391 2.13500 6.78106 0.6307849174478944E-02 -48.4844 0.638788 -50.2328 0.1475147744703220E-01 26.7931 0.402463 26.6713 0.9468437743011001 -19.7387 3.79790 -12.9643 0.2140312299941794E-01 -99.6323 4.49777 -103.660 0.5939959967353488E-01 -81.0910 0.166723 -80.7318 0.2348929157422787 68.1695 0.703209 66.0916 0.7207515678571277E-02 -47.9394 4.57117 -58.5354 0.5944396897656727E-02 -29.6743 4.13215 -35.4477 0.3637663165771322E-01 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 returns values of the Owen T function. H A T 0.625000E-01 0.250000 0.3891193023470137E-01 6.50000 0.437500 0.2000577304850831E-10 7.00000 0.968750 0.6399062719389869E-12 4.78125 0.625000E-01 0.1063297480468746E-06 2.00000 0.500000 0.8625077985521507E-02 1.00000 0.999997 0.6674180897822860E-01 1.00000 0.500000 0.4306469112078537E-01 1.00000 1.00000 0.6674188216570097E-01 1.00000 2.00000 0.7846818699308410E-01 1.00000 3.00000 0.7929950474887260E-01 0.500000 0.500000 0.6448860284750375E-01 0.500000 1.00000 0.1066710629614485 0.500000 2.00000 0.1415806036539784 0.500000 3.00000 0.1510840430760184 0.250000 0.500000 0.7134663382271778E-01 0.250000 1.00000 0.1201285306350883 0.250000 2.00000 0.1666128410939293 0.250000 3.00000 0.1847501847929859 0.125000 0.500000 0.7317273327500386E-01 0.125000 1.00000 0.1237630544953746 0.125000 2.00000 0.1737438887583106 0.125000 3.00000 0.1951190307092811 0.781250E-02 0.500000 0.7378938035365545E-01 0.781250E-02 1.00000 0.1249951430754052 0.781250E-02 2.00000 0.1761984774738108 0.781250E-02 3.00000 0.1987772386442824 0.781250E-02 10.0000 0.2340886964802671 0.781250E-02 100.000 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) 1 0 2 1 4 2 8 4 16 6 32 11 64 18 128 31 256 54 512 97 1024 172 2048 309 4096 564 8192 1028 16384 1900 32768 3512 65536 6542 131072 12251 262144 23000 524288 43390 1048576 82025 POISSON_CDF_VALUES_TEST: POISSON_CDF_VALUES returns values of the Poisson Cumulative Density Function. A X CDF 0.2000E-01 0 0.9801986733067553 0.1000 0 0.9048374180359596 0.1000 1 0.9953211598395555 0.5000 0 0.6065306597126334 0.5000 1 0.9097959895689501 0.5000 2 0.9856123220330293 1.000 0 0.3678794411714423 1.000 1 0.7357588823428846 1.000 2 0.9196986029286058 1.000 3 0.9810118431238462 2.000 0 0.1353352832366127 2.000 1 0.4060058497098381 2.000 2 0.6766764161830635 2.000 3 0.8571234604985470 5.000 0 0.6737946999085467E-02 5.000 1 0.4042768199451280E-01 5.000 2 0.1246520194830811 5.000 3 0.2650259152973617 5.000 4 0.4404932850652124 5.000 5 0.6159606548330631 5.000 6 0.7621834629729387 POLYLOGARITHM_VALUES_TEST: POLYLOGARITHM_VALUES returns values of the polylogarithm. N Z FX 2 1.000 1.644934066848226 3 1.000 1.202056903159594 10 1.000 1.000994575127818 2 0.5000 0.5822405264650125 3 0.5000 0.5372131936080402 10 0.5000 0.5002463206060068 2 0.3333 0.3662132299770635 3 0.3333 0.3488278611548401 10 0.3333 0.3334424797228716 2 0.1000 0.1026177910993911 3 0.1000 0.1012886844792230 10 0.1000 0.1000097826564961 POLYOMINO_CHIRAL_COUNT_VALUES_TEST: POLYOMINO_CHIRAL_COUNT_VALUES returns values of the number of chiral polyominoes of given order. 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 values of the number of fixed polyominoes of given order. 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 values of the number of free polyominoes of given order. 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 returns values of the Prandtl number of water as a function of temperature and pressure. T P Pr(T,P) 0.00000 1.00000 13.5000 0.00000 5.00000 13.4800 0.00000 10.0000 13.4600 0.00000 25.0000 13.3900 0.00000 50.0000 13.2700 0.00000 75.0000 13.1500 0.00000 100.000 13.0400 0.00000 125.000 12.9300 0.00000 150.000 12.8300 0.00000 175.000 12.7300 0.00000 200.000 12.6300 0.00000 225.000 12.5300 0.00000 250.000 12.4300 0.00000 275.000 12.3400 0.00000 300.000 12.2500 0.00000 350.000 12.0800 0.00000 400.000 11.9200 0.00000 450.000 11.7700 0.00000 500.000 11.6200 0.00000 550.000 11.4800 0.00000 600.000 11.3600 0.00000 650.000 11.2300 0.00000 700.000 11.1200 0.00000 800.000 10.9100 0.00000 900.000 10.7200 0.00000 1000.00 10.5500 25.0000 1.00000 6.13700 50.0000 1.00000 3.55500 75.0000 1.00000 2.37800 100.000 1.00000 1.00000 150.000 1.00000 0.974000 200.000 1.00000 0.960000 400.000 1.00000 0.924000 600.000 1.00000 0.899000 800.000 1.00000 0.882000 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 returns values of the saturation pressure of water as a function of temperature. T PSAT(T) 0.100000E-01 0.611730E-02 1.00000 0.657160E-02 5.00000 0.872600E-02 50.0000 0.123440 100.000 1.01320 125.000 2.32010 150.000 4.75720 200.000 15.5370 250.000 39.7370 300.000 85.8380 350.000 165.210 373.976 220.550 PSI_VALUES_TEST: PSI_VALUES returns values of the PSI function. X PSI(X) 0.100000 -10.42375494041108 0.200000 -5.289039896592188 0.300000 -3.502524222200133 0.400000 -2.561384544585116 0.500000 -1.963510026021423 0.600000 -1.540619213893190 0.700000 -1.220023553697935 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.00000 -0.5772156649015329 1.10000 -0.4237549404110768 1.20000 -0.2890398965921883 1.30000 -0.1691908888667997 1.40000 -0.6138454458511615E-01 1.50000 0.3648997397857652E-01 1.60000 0.1260474527734763 1.70000 0.2085478748734940 1.80000 0.2849914332938615 1.90000 0.3561841611640597 2.00000 0.4227843350984671 R8_FACTORIAL_VALUES_TEST: R8_FACTORIAL_VALUES returns values of the factorial function (using real arithmetic). N Factorial(N) 0 1.000000000000000 1 1.000000000000000 2 2.000000000000000 3 6.000000000000000 4 24.00000000000000 5 120.0000000000000 6 720.0000000000000 7 5040.000000000000 8 40320.00000000000 9 362880.0000000000 10 3628800.000000000 11 39916800.00000000 12 479001600.0000000 13 6227020800.000000 14 87178291200.00000 15 1307674368000.000 16 20922789888000.00 17 355687428096000.0 18 6402373705728000. 19 0.1216451004088320E+18 20 0.2432902008176640E+19 25 0.1551121004333099E+26 50 0.3041409320171338E+65 100 0.9332621544394415+158 150 0.5713383956445855+263 R8_FACTORIAL_LOG_VALUES_TEST: R8_FACTORIAL_LOG_VALUES returns values of the logarithm of the factorial function (using real arithmetic). N Log(Factorial(N)) 0 0.000000000000000 1 0.000000000000000 2 0.6931471805599453 3 1.791759469228055 4 3.178053830347946 5 4.787491742782046 6 6.579251212010101 7 8.525161361065415 8 10.60460290274525 9 12.80182748008147 10 15.10441257307552 11 17.50230784587389 12 19.98721449566189 13 22.55216385312342 14 25.19122118273868 15 27.89927138384089 16 30.67186010608067 17 33.50507345013689 18 36.39544520803305 19 39.33988418719949 20 42.33561646075349 25 58.00360522298052 50 148.4777669517730 100 363.7393755555635 150 605.0201058494237 500 2611.330458460156 1000 5912.128178488163 R8_FACTORIAL2_VALUES_TEST: R8_FACTORIAL2_VALUES returns values of the double factorial function (using real arithmetic). N Factorial2(N) 0 1.000000000000000 1 1.000000000000000 2 2.000000000000000 3 3.000000000000000 4 8.000000000000000 5 15.00000000000000 6 48.00000000000000 7 105.0000000000000 8 384.0000000000000 9 945.0000000000000 10 3840.000000000000 11 10395.00000000000 12 46080.00000000000 13 135135.0000000000 14 645120.0000000000 15 2027025.000000000 R8_FALL_VALUES_TEST: R8_FALL_VALUES returns some exact values of the falling factorial function: X N R8_FALL(X,N) 5.0000 4 120.0000 5.2500 4 163.1602 5.5000 4 216.5625 5.7500 4 281.6602 6.0000 4 360.0000 7.5000 0 1.0000 7.5000 1 7.5000 7.5000 2 48.7500 7.5000 3 268.1250 7.5000 4 1206.5625 7.5000 5 4222.9688 7.5000 6 10557.4219 7.5000 7 15836.1328 7.5000 8 7918.0664 7.5000 9 -3959.0332 R8_RISE_VALUES_TEST: R8_RISE_VALUES returns some exact values of the rising factorial function: X N R8_RISE(X,N) 5.0000 4 1680.00 5.2500 4 1962.60 5.5000 4 2279.06 5.7500 4 2631.97 6.0000 4 3024.00 7.5000 0 1.00000 7.5000 1 7.50000 7.5000 2 63.7500 7.5000 3 605.625 7.5000 4 6359.06 7.5000 5 73129.2 7.5000 6 914115. 7.5000 7 0.123406E+08 7.5000 8 0.178938E+09 7.5000 9 0.277354E+10 RAYLEIGH_CDF_VALUES_TEST: RAYLEIGH_CDF_VALUES returns values of the Rayleigh Cumulative Density Function. SIGMA X CDF 0.500000 1.00000 0.8646647167633873 0.500000 2.00000 0.9996645373720975 0.500000 3.00000 0.9999999847700203 0.500000 4.00000 0.9999999999999870 1.00000 2.00000 0.8646647167633873 2.00000 2.00000 0.3934693402873666 3.00000 2.00000 0.1992625970831920 4.00000 2.00000 0.1175030974154046 5.00000 2.00000 0.7688365361336422E-01 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 1.00000 0.500000 0.100000 0.7322491280963244 2.00000 0.500000 0.100000 0.3368973499542734 1.00000 0.500000 0.200000 0.9036119633409063 2.00000 0.500000 0.200000 1.026062482798735 1.00000 0.500000 0.400000 0.5968580144169457 2.00000 0.500000 0.400000 0.8953274901880941 1.00000 1.00000 0.100000 0.8500366602520341E-01 2.00000 1.00000 0.100000 0.4539992976248485E-02 1.00000 1.00000 0.200000 0.3661245640481622 2.00000 1.00000 0.200000 0.1684486749771367 1.00000 1.00000 0.400000 0.4518059816704532 2.00000 1.00000 0.400000 0.5130312413993675 1.00000 2.00000 0.100000 0.8099910956089117E-03 2.00000 2.00000 0.100000 0.4122307244877116E-06 1.00000 2.00000 0.200000 0.4250183301260171E-01 2.00000 2.00000 0.200000 0.2269996488124243E-02 1.00000 2.00000 0.400000 0.1830622820240811 2.00000 2.00000 0.400000 0.8422433748856833E-01 SECVIR_VALUES_TEST: SECVIR_VALUES returns values of the second virial coefficient of water as a function of temperature. T VIR(T) 0.00000 -98.9600 5.00000 -90.0800 10.0000 -82.2900 20.0000 -69.3600 30.0000 -59.1900 40.0000 -51.0700 60.0000 -39.1300 90.0000 -27.8100 120.000 -20.8300 150.000 -16.2100 180.000 -12.9800 210.000 -10.6300 240.000 -8.85000 300.000 -6.39000 400.000 -4.03000 500.000 -2.71000 700.000 -1.32000 1000.00 -0.390000 2000.00 0.530000 SHI_VALUES_TEST: SHI_VALUES returns values of the Hyperbolic Sine Integral function SHI(X). X SHI(X) 0.500000 0.5069967498196672 0.600000 0.6121303965633808 0.700000 0.7193380189288998 0.800000 0.8289965633789345 0.900000 0.9414978265114335 1.00000 1.057250875375729 1.20000 1.300250361022057 1.40000 1.561713388361002 1.60000 1.845814141358504 1.80000 2.157290343425901 2.00000 2.501567433354976 2.50000 3.549340406224435 3.00000 4.973440475859807 3.50000 6.966162067504942 4.00000 9.817326911233033 4.50000 13.96788504934715 SI_VALUES_TEST: SI_VALUES returns 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 1.00000 0.9460830703671830 1.20000 1.108047199013719 1.40000 1.256226732779218 1.60000 1.389180485870438 1.80000 1.505816780255579 2.00000 1.605412976802695 2.50000 1.778520173443827 3.00000 1.848652527999468 3.50000 1.833125398665997 4.00000 1.758203138949053 4.50000 1.654140414379244 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 returns values of the sine function. X SIN(X) 0.00000 0.000000000000000 0.261799 0.2588190451025207 0.500000 0.4794255386042030 0.523599 0.5000000000000000 0.785398 0.7071067811865476 1.00000 0.8414709848078965 1.04720 0.8660254037844386 1.57080 1.000000000000000 2.00000 0.9092974268256817 3.00000 0.1411200080598672 3.14159 0.000000000000000 4.00000 -0.7568024953079282 5.00000 -0.9589242746631385 SIN_DEGREE_VALUES_TEST: SIN_DEGREE_VALUES returns values of the sine function. X SIN_DEGREE(X) -5.00000 -0.8715574274765818E-01 0.00000 0.000000000000000 1.00000 0.1745240643728351E-01 2.00000 0.3489949670250097E-01 3.00000 0.5233595624294383E-01 4.00000 0.6975647374412530E-01 5.00000 0.8715574274765818E-01 10.0000 0.1736481776669304 15.0000 0.2588190451025207 30.0000 0.5000000000000000 45.0000 0.7071067811865476 60.0000 0.8660254037844386 75.0000 0.9659258262890683 85.0000 0.9961946980917455 86.0000 0.9975640502598242 87.0000 0.9986295347545738 88.0000 0.9993908270190958 89.0000 0.9998476951563913 90.0000 1.000000000000000 91.0000 0.9998476951563913 105.000 0.9659258262890683 180.000 0.000000000000000 SIN_POWER_INT_VALUES_TEST: SIN_POWER_INT_VALUES returns values of the integral of SIN(X)^N from A to B. A B N SIN_POWER_INT(A,B,N) 10.0000 20.0000 0 10.0000 0.00000 1.00000 1 0.459698 0.00000 1.00000 2 0.272676 0.00000 1.00000 3 0.178941 0.00000 1.00000 4 0.124026 0.00000 1.00000 5 0.889744E-01 0.00000 2.00000 5 0.903931 1.00000 2.00000 5 0.814957 0.00000 1.00000 10 0.218875E-01 0.00000 1.00000 11 0.170234E-01 SINH_VALUES_TEST: SINH_VALUES returns values of the hyperbolic sine function. X SINH(X) -5.00000 -74.20321057778875 -1.00000 -1.175201193643801 0.00000 0.000000000000000 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 1.026516725708175 1.00000 1.175201193643801 2.00000 3.626860407847019 3.00000 10.01787492740990 4.00000 27.28991719712775 5.00000 74.20321057778875 10.0000 11013.23287470339 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 0.3490905138373300E-01 2.00 8.00 7.00 6.50 7.50 7.50 -0.3743025039659792E-01 3.00 8.00 7.00 6.50 7.50 7.50 0.1890866390959560E-01 4.00 8.00 7.00 6.50 7.50 7.50 0.7342448254928643E-02 5.00 8.00 7.00 6.50 7.50 7.50 -0.2358935185081794E-01 6.00 8.00 7.00 6.50 7.50 7.50 0.1913476955215437E-01 7.00 8.00 7.00 6.50 7.50 7.50 0.1288017397724172E-02 8.00 8.00 7.00 6.50 7.50 7.50 -0.1930018366290527E-01 9.00 8.00 7.00 6.50 7.50 7.50 0.1677305949382889E-01 10.00 8.00 7.00 6.50 7.50 7.50 0.5501147274850949E-02 11.00 8.00 7.00 6.50 7.50 7.50 -0.2135439790896831E-01 12.00 8.00 7.00 6.50 7.50 7.50 0.3460364451435387E-02 13.00 8.00 7.00 6.50 7.50 7.50 0.2520950054795585E-01 14.00 8.00 7.00 6.50 7.50 7.50 0.1483990561221713E-01 15.00 8.00 7.00 6.50 7.50 7.50 0.2708577680633186E-02 SOUND_VALUES_TEST: SOUND_VALUES returns values of the spead of sound in water as a function of temperature and pressure. T P C(T,P) 0.00000 1.00000 1401.00 100.000 1.00000 472.800 200.000 1.00000 533.700 300.000 1.00000 585.700 350.000 1.00000 609.500 400.000 1.00000 632.200 500.000 1.00000 674.600 600.000 1.00000 713.900 850.000 1.00000 802.000 1100.00 1.00000 880.100 1600.00 1.00000 1017.80 2000.00 1.00000 1115.90 0.00000 5.00000 1401.70 0.00000 10.0000 1402.60 0.00000 50.0000 1409.60 0.00000 100.000 1418.10 0.00000 250.000 1443.10 0.00000 500.000 1484.60 0.00000 1000.00 1577.10 0.00000 2500.00 1913.40 SPHERE_UNIT_AREA_VALUES_TEST: SPHERE_UNIT_AREA_VALUES returns values of the area of the unit sphere in various dimensions. N Area 1 2.000000000000000 2 6.283185307179586 3 12.56637061435917 4 19.73920880217872 5 26.31894506957162 6 31.00627668029982 7 33.07336179231981 8 32.46969701133415 9 29.68658012464836 10 25.50164039877345 11 20.72514267328890 12 16.02315322625507 13 11.83817381218268 14 8.389703410491089 15 5.721649212349567 16 3.765290085742291 17 2.396678817591364 18 1.478625959000308 19 0.8858104195716824 20 0.5161378278002812 SPHERE_UNIT_VOLUME_VALUES_TEST: SPHERE_UNIT_VOLUME_VALUES returns values of the volume of the unit sphere in various dimensions. N Volume 1 2.000000000000000 2 3.141592653589793 3 4.188790204786391 4 4.934802200544679 5 5.263789013914325 6 5.167712780049970 7 4.724765970331401 8 4.058712126416768 9 3.298508902738707 10 2.550164039877345 11 1.884103879389900 12 1.335262768854589 13 0.9106287547832831 14 0.5992645293207921 15 0.3814432808233045 16 0.2353306303588932 17 0.1409811069171390 18 0.8214588661112823E-01 19 0.4662160103008855E-01 20 0.2580689139001406E-01 SPHERICAL_HARMONIC_VALUES_TEST: SPHERICAL_HARMONIC_VALUES returns values of the spherical harmonic functions. L M THETA PHI Yr Yi 0 0 0.5236 1.0472 0.2820947917738781 0.000000000000000 1 0 0.5236 1.0472 0.4231421876608172 0.000000000000000 2 1 0.5236 1.0472 -0.1672616358893223 -0.2897056515173922 3 2 0.5236 1.0472 -0.1106331731112457 0.1916222768312404 4 3 0.5236 1.0472 0.1354974113737760 0.000000000000000 5 5 0.2618 0.6283 0.5390423109043568E-03 0.000000000000000 5 4 0.2618 0.6283 -0.5146690442951909E-02 0.3739289485283311E-02 5 3 0.2618 0.6283 0.1371004361349490E-01 -0.4219517552320796E-01 5 2 0.2618 0.6283 0.6096352022265540E-01 0.1876264225575173 5 1 0.2618 0.6283 -0.4170400640977983 -0.3029973424491321 4 2 0.6283 0.7854 0.000000000000000 0.4139385503112256 4 2 1.8850 0.7854 0.000000000000000 -0.1003229830187463 4 2 3.1416 0.7854 0.000000000000000 0.000000000000000 4 2 4.3982 0.7854 0.000000000000000 -0.1003229830187463 4 2 5.6549 0.7854 0.000000000000000 0.4139385503112256 3 -1 0.3927 0.4488 0.3641205966137958 -0.1753512375142586 3 -1 0.3927 0.8976 0.2519792711195075 -0.3159720118970196 3 -1 0.3927 1.3464 0.8993036065704300E-01 -0.3940106541811563 3 -1 0.3927 1.7952 -0.8993036065704300E-01 -0.3940106541811563 3 -1 0.3927 2.2440 -0.2519792711195075 -0.3159720118970196 SQRT_VALUES_TEST: SQRT evaluates the square root function. SQRT_VALUES returns some exact values. X SQRT(X) 0.0000 0.00000 0.0000 0.900000E-04 0.0900 0.300000 0.1000 0.316228 0.4000 0.632456 1.0000 1.00000 2.0000 1.41421 3.0000 1.73205 3.1416 1.77245 19.0000 4.35890 29.0000 5.38516 71.0000 8.42615 97.0000 9.84886 123456789.0000 11111.1 STIRLING1_VALUES_TEST: STIRLING1_VALUES returns values of the Stirling numbers of the first kind. N M S1(N,M) 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 first kind. N M S2(N,M) 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 returns values of the Stromgen function. X F(X) 0.195312E-02 0.2190106598569866E-15 0.781250E-02 0.2248139943862525E-12 0.312500E-01 0.2324501957955886E-09 0.125000 0.2471956147597501E-06 0.500000 0.2899261098983324E-03 1.00000 0.1069814639080971E-01 1.50000 0.8970765096442473E-01 2.00000 0.4004960571959289 3.00000 3.050410439807909 4.00000 11.36770485843943 4.12500 12.96067940532479 4.50000 18.54871394474851 5.00000 27.86627382190312 6.00000 51.96333407169932 8.00000 108.6101674789123 10.0000 153.7890331655662 15.0000 193.0266553255872 20.0000 196.3685016600654 30.0000 196.5194676600821 50.0000 196.5195692086832 STRUVE_H0_VALUES_TEST: STRUVE_H0_VALUES returns values of the Struve H0 function. X H0(X) 0.195312E-02 0.124340E-02 -0.781250E-02 -0.497356E-02 0.625000E-01 0.397715E-01 -0.250000 -0.158052 1.00000 0.568657 1.25000 0.665984 2.00000 0.790859 -4.00000 -0.135015 7.50000 0.200865 11.0000 -0.111421 11.5000 -0.170268 -16.0000 -0.135449 20.0000 0.943937E-01 25.0000 -0.101825 -30.0000 0.960984E-01 50.0000 -0.853377E-01 75.0000 -0.768823E-01 -80.0000 0.476638E-01 100.000 -0.708788E-01 -125.000 0.657529E-01 STRUVE_H1_VALUES_TEST: STRUVE_H1_VALUES returns values of the Struve H1 function. X H1(X) 0.195312E-02 0.809504E-06 -0.781250E-02 0.129520E-04 0.625000E-01 0.828716E-03 -0.250000 0.132077E-01 1.00000 0.198457 1.25000 0.298538 2.00000 0.646764 -4.00000 1.06973 7.50000 0.388313 11.0000 0.748542 11.5000 0.846649 -16.0000 0.583857 20.0000 0.806006 25.0000 0.538804 -30.0000 0.721750 50.0000 0.580078 75.0000 0.601519 -80.0000 0.706115 100.000 0.616311 -125.000 0.627785 STRUVE_L0_VALUES_TEST: STRUVE_L0_VALUES returns values of the Struve L0 function. X L0(X) 0.195312E-02 0.124340E-02 -0.312500E-01 -0.198965E-01 0.125000 0.797157E-01 -0.500000 -0.327241 1.00000 0.710243 2.00000 1.93743 -4.00000 -11.1311 7.00000 168.501 -10.0000 -2815.65 16.0000 893446. 16.2500 0.113820E+07 -17.0000 -0.235497E+07 20.0000 0.435583E+08 22.5000 0.499935E+09 -25.0000 -0.577456E+10 30.0000 0.781672E+12 -40.0000 -0.148948E+17 50.0000 0.293255E+21 60.0000 0.589408E+25 -70.0000 -0.120159E+30 STRUVE_L1_VALUES_TEST: STRUVE_L1_VALUES returns values of the Struve L1 function. X L1(X) 0.195312E-02 0.809504E-06 -0.312500E-01 0.207246E-03 0.125000 0.331918E-02 -0.500000 0.539422E-01 1.00000 0.226764 2.00000 1.10276 -4.00000 9.16928 7.00000 155.417 -10.0000 2670.36 16.0000 865059. 16.2500 0.110260E+07 -17.0000 0.228462E+07 20.0000 0.424550E+08 22.5000 0.488696E+09 -25.0000 0.565787E+10 30.0000 0.768532E+12 -40.0000 0.147074E+17 50.0000 0.290308E+21 60.0000 0.584475E+25 -70.0000 0.119298E+30 STUDENT_CDF_VALUES_TEST: STUDENT_CDF_VALUES returns values of the Student T Cumulative Density Function. C X CDF 1.000 0.3250 0.6000231200328521 2.000 0.2890 0.6001080279134390 3.000 0.2770 0.6001150934648930 4.000 0.2710 0.6000995134721354 5.000 0.2670 0.5999341989834830 2.000 0.8160 0.7498859393137811 5.000 0.7270 0.7500879487671045 2.000 2.920 0.9500004222186464 5.000 2.015 0.9499969138365968 2.000 6.965 0.9900012348724744 3.000 4.541 0.9900017619355059 4.000 3.747 0.9900004567580596 5.000 3.365 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 3.000 0.000 1 0.897584 3.000 0.000 2 0.952267 3.000 0.000 3 0.971166 3.000 0.5000 1 0.823122 3.000 0.5000 2 0.904902 3.000 0.5000 3 0.936347 3.000 1.000 1 0.730103 3.000 1.000 2 0.833559 3.000 1.000 3 0.877401 3.000 2.000 1 0.524857 3.000 2.000 2 0.629386 3.000 2.000 3 0.680027 3.000 4.000 1 0.205901 3.000 4.000 2 0.211215 3.000 4.000 3 0.207473 15.00 7.000 15 0.998113 15.00 7.000 20 0.999487 15.00 7.000 25 0.999839 0.5000E-01 1.000 1 0.168611 0.5000E-01 1.000 2 0.169680 0.5000E-01 1.000 3 0.170104 4.000 2.000 10 0.924768 4.000 3.000 10 0.748314 4.000 4.000 10 0.465980 5.000 2.000 10 0.976187 5.000 3.000 10 0.897969 5.000 4.000 10 0.718190 6.000 2.000 10 0.992366 6.000 3.000 10 0.961034 6.000 4.000 10 0.868801 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 returns values of the surface tension of water as a function of temperature. T SIGMA(T) 10.0000 74.2200 20.0000 72.7400 30.0000 71.2000 40.0000 69.6000 50.0000 67.9500 100.000 58.9200 150.000 48.7500 200.000 37.6800 250.000 26.0500 300.000 14.3700 325.000 8.78000 350.000 3.67000 370.000 0.400000 373.976 0.00000 SYNCH1_VALUES_TEST: SYNCH1_VALUES returns values of the synchrotron radiation function. X S1(X) 0.195312E-02 0.265149 0.312500E-01 0.620501 0.125000 0.851126 0.500000 0.870819 1.00000 0.651423 1.50000 0.450640 2.00000 0.301636 2.50000 0.198145 3.00000 0.128566 4.00000 0.528274E-01 4.25000 0.421393E-01 5.00000 0.212481E-01 5.50000 0.134003E-01 6.00000 0.842608E-02 8.00000 0.128845E-02 10.0000 0.192238E-03 12.0000 0.282211E-04 15.0000 0.155488E-05 20.0000 0.119686E-07 25.0000 0.895642E-10 SYNCH2_VALUES_TEST: SYNCH2_VALUES returns values of the synchrotron radiation function. X S2(X) 0.195312E-02 0.134307 0.312500E-01 0.334853 0.125000 0.504042 0.500000 0.602965 1.00000 0.494475 1.50000 0.360361 2.00000 0.249678 2.50000 0.168138 3.00000 0.111171 4.00000 0.469232E-01 4.25000 0.376245E-01 5.00000 0.192221E-01 5.50000 0.122095E-01 6.00000 0.772496E-02 8.00000 0.120290E-02 10.0000 0.181612E-03 12.0000 0.268843E-04 15.0000 0.149422E-05 20.0000 0.116077E-07 25.0000 0.873623E-10 tan_values_test(): tan_values() returns values of the tangent function. X TAN(X) 0.00000 0.000000000000000 0.261799 0.2679491924311227 0.500000 0.5463024898437905 0.523599 0.5773502691896257 0.785398 1.000000000000000 1.00000 1.557407724654902 1.04720 1.732050807568877 1.30900 3.732050807568877 1.43990 7.595754112725150 1.50535 15.25705168826554 2.00000 -2.185039863261519 3.00000 -0.1425465430742778 3.14159 0.000000000000000 4.00000 1.157821282349577 5.00000 -3.380515006246586 TANH_VALUES_TEST: TANH_VALUES returns values of the hyperbolic tangent function. X TANH(X) -5.00000 -0.9999092042625951 -1.00000 -0.7615941559557649 0.00000 0.000000000000000 0.100000 0.9966799462495582E-01 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 1.00000 0.7615941559557649 2.00000 0.9640275800758169 3.00000 0.9950547536867305 4.00000 0.9993292997390670 5.00000 0.9999092042625951 10.0000 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 returns values of the thermal conductivity of water as a function of temperature and pressure. T P LAMBDA(T,P) 0.00000 1.00000 561.000 0.00000 5.00000 561.300 0.00000 10.0000 561.500 0.00000 25.0000 562.400 0.00000 50.0000 563.700 0.00000 75.0000 565.100 0.00000 100.000 566.500 0.00000 125.000 567.900 0.00000 150.000 569.300 0.00000 175.000 570.600 0.00000 200.000 572.000 0.00000 225.000 573.400 0.00000 250.000 574.800 0.00000 275.000 576.100 0.00000 300.000 577.500 0.00000 350.000 580.200 0.00000 400.000 582.900 0.00000 450.000 585.500 0.00000 500.000 588.100 0.00000 550.000 590.700 0.00000 600.000 593.300 0.00000 650.000 595.800 0.00000 700.000 598.300 0.00000 800.000 603.100 0.00000 900.000 607.800 0.00000 1000.00 612.200 25.0000 1.00000 607.200 50.0000 1.00000 643.600 75.0000 1.00000 666.800 100.000 1.00000 25.0800 150.000 1.00000 28.8500 200.000 1.00000 33.2800 400.000 1.00000 54.7600 600.000 1.00000 79.8900 800.000 1.00000 107.300 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 -0.9534625892455922E-01 3.00 4.50 3.50 1.00 -3.50 2.50 -0.6741998624632421E-01 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 -0.5536235693131719E-01 8.00 4.50 3.50 1.00 -3.50 2.50 0.1799835451137786E-01 TRAN02_VALUES_TEST: TRAN02_VALUES returns values of the order 2 transportation function. X T2(X) 0.195312E-02 0.195312E-02 0.312500E-01 0.312492E-01 0.125000 0.124946 0.500000 0.496554 1.00000 0.973033 1.50000 1.41220 2.00000 1.80172 2.50000 2.13504 3.00000 2.41105 4.00000 2.80667 4.25000 2.87774 5.00000 3.03917 5.50000 3.11251 6.00000 3.16567 8.00000 3.26235 10.0000 3.28433 15.0000 3.28979 20.0000 3.28987 30.0000 3.28987 50.0000 3.28987 TRAN03_VALUES_TEST: TRAN03_VALUES returns values of the order 3 transportation function. X T3(X) 0.195312E-02 0.190735E-05 0.312500E-01 0.488261E-03 0.125000 0.780742E-02 0.500000 0.123709 1.00000 0.479841 1.50000 1.02694 2.00000 1.70635 2.50000 2.45392 3.00000 3.21060 4.00000 4.57922 4.25000 4.87220 5.00000 5.61439 5.50000 5.99845 6.00000 6.30340 8.00000 6.95799 10.0000 7.15032 15.0000 7.21107 20.0000 7.21232 30.0000 7.21234 50.0000 7.21234 TRAN04_VALUES_TEST: TRAN04_VALUES returns values of the order 4 transportation function. X T4(X) 0.195312E-02 0.248353E-08 0.312500E-01 0.101720E-04 0.125000 0.650533E-03 0.500000 0.411504E-01 1.00000 0.317244 1.50000 1.00794 2.00000 2.20109 2.50000 3.88465 3.00000 5.96482 4.00000 10.7319 4.25000 11.9400 5.00000 15.3598 5.50000 17.3726 6.00000 19.1230 8.00000 23.5840 10.0000 25.2737 15.0000 25.9552 20.0000 25.9754 30.0000 25.9758 50.0000 25.9758 TRAN05_VALUES_TEST: TRAN05_VALUES returns values of the order 5 transportation function. X T5(X) 0.195312E-02 0.363798E-11 0.312500E-01 0.238406E-06 0.125000 0.609822E-04 0.500000 0.154100E-01 1.00000 0.236616 1.50000 1.11988 2.00000 3.22929 2.50000 7.03630 3.00000 12.7706 4.00000 29.4883 4.25000 34.4713 5.00000 50.2631 5.50000 60.8199 6.00000 70.8733 8.00000 101.478 10.0000 116.381 15.0000 124.096 20.0000 124.423 30.0000 124.431 50.0000 124.431 TRAN06_VALUES_TEST: TRAN06_VALUES returns values of the order 6 transportation function. X T6(X) 0.195312E-02 0.568434E-14 0.312500E-01 0.596012E-08 0.125000 0.609784E-05 0.500000 0.615789E-02 1.00000 0.188544 1.50000 1.33193 2.00000 5.08572 2.50000 13.7292 3.00000 29.5796 4.00000 88.6008 4.25000 109.160 5.00000 182.243 5.50000 237.654 6.00000 295.432 8.00000 506.812 10.0000 638.782 15.0000 726.992 20.0000 732.303 30.0000 732.487 50.0000 732.487 TRAN07_VALUES_TEST: TRAN07_VALUES returns values of the order 7 transportation function. X T7(X) 0.195312E-02 0.925186E-17 0.312500E-01 0.155211E-09 0.125000 0.635162E-06 0.500000 0.256388E-02 1.00000 0.156653 1.50000 1.65382 2.00000 8.37631 2.50000 28.0786 3.00000 72.0097 4.00000 281.749 4.25000 366.602 5.00000 705.561 5.50000 996.619 6.00000 1328.89 8.00000 2798.76 10.0000 3972.14 15.0000 4991.35 20.0000 5078.16 30.0000 5082.08 50.0000 5082.08 TRAN08_VALUES_TEST: TRAN08_VALUES returns values of the order 8 transportation function. X T8(X) 0.195312E-02 0.154886E-19 0.312500E-01 0.415743E-11 0.125000 0.680507E-07 0.500000 0.109817E-02 1.00000 0.133964 1.50000 2.11534 2.00000 14.2279 2.50000 59.3121 3.00000 181.396 4.00000 931.480 4.25000 1281.79 5.00000 2857.28 5.50000 4387.30 6.00000 6299.32 8.00000 16589.4 10.0000 27064.8 15.0000 38974.6 20.0000 40400.2 30.0000 40484.3 50.0000 40484.4 TRAN09_VALUES_TEST: TRAN09_VALUES returns values of the order 9 transportation function. X T9(X) 0.195312E-02 0.264698E-22 0.312500E-01 0.113679E-12 0.125000 0.744282E-08 0.500000 0.480227E-03 1.00000 0.117002 1.50000 2.76490 2.00000 24.7166 2.50000 128.271 3.00000 468.429 4.00000 3167.40 4.25000 4614.09 5.00000 11952.7 5.50000 20001.6 6.00000 31011.1 8.00000 103529. 10.0000 197432. 15.0000 338260. 20.0000 361796. 30.0000 363606. 50.0000 363609. TRIGAMMA_VALUES_TEST: TRIGAMMA_VALUES returns values of the TriGamma function. X F(X) 1.00000 1.644934066848226 1.10000 1.433299150792759 1.20000 1.267377205423779 1.30000 1.134253434996619 1.40000 1.025356590529597 1.50000 0.9348022005446793 1.60000 0.8584318931245799 1.70000 0.7932328301639984 1.80000 0.7369741375017002 1.90000 0.6879720582426356 2.00000 0.6449340668482264 TRUNCATED_NORMAL_AB_CDF_VALUES_TEST: TRUNCATED_NORMAL_AB_CDF_VALUES returns values of the truncated Normal CDF. MU SIGMA A B X CDF 100.0 25.0 50.0 150.0 90.0 0.3371694242213513 100.0 25.0 50.0 150.0 92.0 0.3685009225506048 100.0 25.0 50.0 150.0 94.0 0.4006444233448185 100.0 25.0 50.0 150.0 96.0 0.4334107066903040 100.0 25.0 50.0 150.0 98.0 0.4665988676496338 100.0 25.0 50.0 150.0 100.0 0.5000000000000000 100.0 25.0 50.0 150.0 102.0 0.5334011323503662 100.0 25.0 50.0 150.0 104.0 0.5665892933096960 100.0 25.0 50.0 150.0 106.0 0.5993555766551815 100.0 25.0 50.0 150.0 108.0 0.6314990774493952 100.0 25.0 50.0 150.0 110.0 0.6628305757786487 TRUNCATED_NORMAL_AB_PDF_VALUES_TEST: TRUNCATED_NORMAL_AB_PDF_VALUES returns values of the truncated Normal PDF. MU SIGMA A B X PDF 100.0 25.0 50.0 150.0 90.0 0.1543301171801836E-01 100.0 25.0 50.0 150.0 92.0 0.1588394472270638E-01 100.0 25.0 50.0 150.0 94.0 0.1624375997031919E-01 100.0 25.0 50.0 150.0 96.0 0.1650575046469259E-01 100.0 25.0 50.0 150.0 98.0 0.1666496869385951E-01 100.0 25.0 50.0 150.0 100.0 0.1671838200940538E-01 100.0 25.0 50.0 150.0 102.0 0.1666496869385951E-01 100.0 25.0 50.0 150.0 104.0 0.1650575046469259E-01 100.0 25.0 50.0 150.0 106.0 0.1624375997031919E-01 100.0 25.0 50.0 150.0 108.0 0.1588394472270638E-01 100.0 25.0 50.0 150.0 110.0 0.1543301171801836E-01 TRUNCATED_NORMAL_A_CDF_VALUES_TEST: TRUNCATED_NORMAL_A_CDF_VALUES returns values of the lower truncated Normal CDF. MU SIGMA A X CDF 100.0 25.0 50.0 90.0 0.3293202045481688 100.0 25.0 50.0 92.0 0.3599223134505957 100.0 25.0 50.0 94.0 0.3913175216041539 100.0 25.0 50.0 96.0 0.4233210140873113 100.0 25.0 50.0 98.0 0.4557365629792204 100.0 25.0 50.0 100.0 0.4883601253415709 100.0 25.0 50.0 102.0 0.5209836877039214 100.0 25.0 50.0 104.0 0.5533992365958303 100.0 25.0 50.0 106.0 0.5854027290789878 100.0 25.0 50.0 108.0 0.6167979372325459 100.0 25.0 50.0 110.0 0.6474000461349729 TRUNCATED_NORMAL_A_PDF_VALUES_TEST: TRUNCATED_NORMAL_A_PDF_VALUES returns values of the lower Truncated Normal PDF. MU SIGMA A X PDF 100.0 25.0 50.0 90.0 0.1507373507401876E-01 100.0 25.0 50.0 92.0 0.1551417047139894E-01 100.0 25.0 50.0 94.0 0.1586560931024694E-01 100.0 25.0 50.0 96.0 0.1612150073158793E-01 100.0 25.0 50.0 98.0 0.1627701240029317E-01 100.0 25.0 50.0 100.0 0.1632918226724295E-01 100.0 25.0 50.0 102.0 0.1627701240029317E-01 100.0 25.0 50.0 104.0 0.1612150073158793E-01 100.0 25.0 50.0 106.0 0.1586560931024694E-01 100.0 25.0 50.0 108.0 0.1551417047139894E-01 100.0 25.0 50.0 110.0 0.1507373507401876E-01 TRUNCATED_NORMAL_B_CDF_VALUES_TEST: TRUNCATED_NORMAL_B_CDF_VALUES returns values of the upper truncated Normal CDF. MU SIGMA B X CDF 100.0 25.0 150.0 90.0 0.3525999538650271 100.0 25.0 150.0 92.0 0.3832020627674540 100.0 25.0 150.0 94.0 0.4145972709210122 100.0 25.0 150.0 96.0 0.4466007634041696 100.0 25.0 150.0 98.0 0.4790163122960786 100.0 25.0 150.0 100.0 0.5116398746584291 100.0 25.0 150.0 102.0 0.5442634370207796 100.0 25.0 150.0 104.0 0.5766789859126887 100.0 25.0 150.0 106.0 0.6086824783958461 100.0 25.0 150.0 108.0 0.6400776865494043 100.0 25.0 150.0 110.0 0.6706797954518312 TRUNCATED_NORMAL_B_PDF_VALUES_TEST: TRUNCATED_NORMAL_B_PDF_VALUES returns values of the upper truncated Normal PDF. MU SIGMA B X PDF 100.0 25.0 150.0 90.0 0.1507373507401876E-01 100.0 25.0 150.0 92.0 0.1551417047139894E-01 100.0 25.0 150.0 94.0 0.1586560931024694E-01 100.0 25.0 150.0 96.0 0.1612150073158793E-01 100.0 25.0 150.0 98.0 0.1627701240029317E-01 100.0 25.0 150.0 100.0 0.1632918226724295E-01 100.0 25.0 150.0 102.0 0.1627701240029317E-01 100.0 25.0 150.0 104.0 0.1612150073158793E-01 100.0 25.0 150.0 106.0 0.1586560931024694E-01 100.0 25.0 150.0 108.0 0.1551417047139894E-01 100.0 25.0 150.0 110.0 0.1507373507401876E-01 TSAT_VALUES_TEST: TSAT_VALUES returns values of the saturation temperature as a function of pressure. P Tsat(P) 0.611730E-02 0.100000E-01 0.120000E-01 9.65500 0.250000E-01 21.0800 0.550000E-01 34.5890 0.800000E-01 41.5180 0.110000 47.6950 0.160000 55.3270 0.250000 64.9800 0.500000 81.3390 0.750000 91.7830 1.00000 99.6320 1.50000 111.378 2.00000 120.443 5.00000 151.866 10.0000 179.916 20.0000 212.417 50.0000 263.977 100.000 311.031 200.000 365.800 220.550 373.976 VAN_DER_CORPUT_VALUES_TEST: VAN_DER_CORPUT_VALUES returns values of the van der Corput sequence in a given base. BASE SEED VDC(BASE,SEED) 2 0 0.0000000 2 1 0.50000000 2 2 0.25000000 2 3 0.75000000 2 4 0.12500000 2 5 0.62500000 2 6 0.37500000 2 7 0.87500000 2 8 0.62500000E-01 3 0 0.0000000 3 1 0.33333333 3 2 0.66666667 3 3 0.11111111 3 4 0.44444444 3 5 0.77777778 3 6 0.22222222 3 7 0.55555556 3 8 0.88888889 4 0 0.0000000 4 1 0.25000000 4 2 0.50000000 4 3 0.75000000 4 4 0.62500000E-01 4 5 0.31250000 4 6 0.56250000 4 7 0.81250000 4 8 0.12500000 2 10 0.31250000 3 10 0.37037037 4 10 0.62500000 5 10 0.80000000E-01 7 10 0.44897959 11 10 0.90909091 13 10 0.76923077 2 100 0.14843750 3 100 0.41152263 4 100 0.97656250E-01 5 100 0.32000000E-01 7 100 0.29154519 11 100 0.16528926 13 100 0.73372781 2 1000 0.92773438E-01 3 1000 0.34750800 4 1000 0.17089844 5 1000 0.51200000E-02 7 1000 0.91628488 11 1000 0.93163035 13 1000 0.99044151 2 10000 0.34729004E-01 3 10000 0.38612000 4 10000 0.18920898E-01 5 10000 0.51200000E-03 7 10000 0.57499851 11 10000 0.15299501 13 10000 0.24592976 29 1000 0.48874493 29 1001 0.52322768 29 1002 0.55771044 29 1003 0.59219320 29 1004 0.62667596 71 1000 0.87284269E-01 71 1001 0.10136878 71 1002 0.11545328 71 1003 0.12953779 71 1004 0.14362230 173 1000 0.78051388 173 1001 0.78629423 173 1002 0.79207458 173 1003 0.79785492 173 1004 0.80363527 409 1000 0.44499973 409 1001 0.44744472 409 1002 0.44988971 409 1003 0.45233469 409 1004 0.45477968 VISCOSITY_VALUES_TEST: VISCOSITY_VALUES returns values of the viscosity of water as a function of temperature and pressure. T P ETA(T,P) 0.00000 1.00000 1792.00 0.00000 5.00000 1791.00 0.00000 10.0000 1790.00 0.00000 25.0000 1786.00 0.00000 50.0000 1780.00 0.00000 75.0000 1775.00 0.00000 100.000 1769.00 0.00000 125.000 1764.00 0.00000 150.000 1759.00 0.00000 175.000 1754.00 0.00000 200.000 1749.00 0.00000 225.000 1744.00 0.00000 250.000 1739.00 0.00000 275.000 1735.00 0.00000 300.000 1731.00 0.00000 350.000 1722.00 0.00000 400.000 1714.00 0.00000 450.000 1707.00 0.00000 500.000 1700.00 0.00000 550.000 1694.00 0.00000 600.000 1687.00 0.00000 650.000 1682.00 0.00000 700.000 1676.00 0.00000 800.000 1667.00 0.00000 900.000 1659.00 0.00000 1000.00 1653.00 25.0000 1.00000 890.800 50.0000 1.00000 547.100 75.0000 1.00000 378.400 100.000 1.00000 12.2800 200.000 1.00000 16.1800 400.000 1.00000 24.4500 600.000 1.00000 32.6100 800.000 1.00000 40.3800 VON_MISES_CDF_VALUES_TEST: VON_MISES_CDF_VALUES returns values of the von Mises CDF. A B X CDF 0.00000 1.00000 -2.61799 0.253509E-01 0.00000 1.00000 -1.57080 0.109754 0.00000 1.00000 0.00000 0.500000 0.00000 1.00000 1.04720 0.804338 0.00000 1.00000 2.09440 0.941746 1.00000 2.00000 1.00000 0.500000 1.00000 2.00000 1.20000 0.601820 1.00000 2.00000 1.40000 0.695936 1.00000 2.00000 1.60000 0.776594 1.00000 2.00000 1.80000 0.841073 1.00000 2.00000 2.00000 0.889578 -2.00000 3.00000 0.00000 0.996032 -1.00000 3.00000 0.00000 0.940434 0.00000 3.00000 0.00000 0.500000 1.00000 3.00000 0.00000 0.595664E-01 2.00000 3.00000 0.00000 0.396773E-02 3.00000 3.00000 0.00000 0.232195E-03 0.00000 0.00000 0.785398 0.625000 0.00000 1.00000 0.785398 0.743841 0.00000 2.00000 0.785398 0.836922 0.00000 3.00000 0.785398 0.894171 0.00000 4.00000 0.785398 0.929106 0.00000 5.00000 0.785398 0.951429 WEEKDAY_VALUES_TEST: WEEKDAY_VALUES returns 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 returns values of the Weibull Cumulative Density Function. ALPHA BETA X CDF 1.00000 0.500000 1.00000 0.8646647167633873 1.00000 0.500000 2.00000 0.9816843611112658 1.00000 0.500000 3.00000 0.9975212478233336 1.00000 0.500000 4.00000 0.9996645373720975 1.00000 2.00000 2.00000 0.6321205588285577 1.00000 3.00000 2.00000 0.4865828809674080 1.00000 4.00000 2.00000 0.3934693402873666 1.00000 5.00000 2.00000 0.3296799539643607 2.00000 2.00000 3.00000 0.8946007754381357 3.00000 2.00000 3.00000 0.9657818816883340 4.00000 2.00000 3.00000 0.9936702845725143 5.00000 2.00000 3.00000 0.9994964109502630 wright_omega_values_test(): wright_omega_values() returns values of the Wright Omega function with complex argument Z FZ 0.00000 0.00000 0.5671432904097838 0.000000000000000 1.00000 0.00000 1.000000000000000 0.000000000000000 3.71828 0.00000 2.718281828459045 0.000000000000000 -1.00000 3.14159 -1.000000000000000 0.000000000000000 -1.00000 -3.14159 -1.000000000000000 0.000000000000000 -1.30685 3.14159 -2.000000000000000 0.000000000000000 -1.30685 -3.14159 -0.4063757399599600 0.000000000000000 0.00000 2.57080 0.000000000000000 1.000000000000000 0.00000 3.14159 -0.3181315052047641 1.337235701430689 1.00000 1.00000 0.9372082083733697 0.5054213160131512 zeta_values_test(): zeta_values() returns values of the Riemann Zeta function. N ZETA(N) 2 1.644934066848226 3 1.202056903159594 4 1.082323233711138 5 1.036927755143370 6 1.017343061984449 7 1.008349277381923 8 1.004077356197944 9 1.002008392926082 10 1.000994575127818 11 1.000494188604119 12 1.000246086553308 16 1.000015282259409 20 1.000000953962034 30 1.000000000931327 40 1.000000000000909 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 0.8232323371113819E-01 5.00 0.3692775514336993E-01 6.00 0.1734306198444914E-01 7.00 0.8349277381922827E-02 8.00 0.4077356197944340E-02 9.00 0.2008392926082214E-02 10.00 0.9945751278180853E-03 11.00 0.4941886041194645E-03 12.00 0.2460865533080483E-03 16.00 0.1528225940865187E-04 20.00 0.9539620338728000E-06 30.00 0.9313274324200000E-10 40.00 0.9094947800000000E-12 test_values_test(): Normal end of execution. 28 December 2023 2:12:23.635 PM