Tue Mar 19 11:19:33 2024 test_values_test(): Python version: 3.8.10 Test test_values(). abram0_values_test(): abram0_values() stores values of the Abramowitz function of order 0. X FX 0.001953 0.8737772630698536 0.007812 0.8472185965045692 0.031250 0.7728893448398830 0.125000 0.5968434585345015 0.500000 0.2987173528367589 1.000000 0.1500459645051639 1.250000 0.1111466241915796 1.500000 0.0839095671531519 1.875000 0.0565523217179434 2.000000 0.0498764966030338 2.125000 0.0441008892197628 3.000000 0.0197385351802541 4.000000 0.0086193088287161 5.000000 0.0040224788162540 6.000000 0.0019718658458165 7.000000 0.0010045868340134 10.000000 0.0001572691726330 15.000000 0.0000103526669124 20.000000 0.0000009122975919 40.000000 0.0000000002562829 abram1_values_test(): abram1_values() stores values of the Abramowitz function of order 1. X FX 0.001953 0.4982821984879992 0.007812 0.4932439177304729 0.031250 0.4743161278469123 0.125000 0.4109598325876041 0.500000 0.2531761738822704 1.000000 0.1465633813859778 1.250000 0.1142154705601837 1.500000 0.0900263073834838 1.875000 0.0640882141707423 2.000000 0.0574466143141662 2.125000 0.0515816245648007 3.000000 0.0252637195557764 4.000000 0.0119308033301966 5.000000 0.0059270542280915 6.000000 0.0030609215358018 7.000000 0.0016307382136980 10.000000 0.0002837185191696 15.000000 0.0000211221501213 20.000000 0.0000020344578893 40.000000 0.0000000007111652 abram2_values_test(): abram2_values() stores values of the Abramowitz function of order 2. X FX 0.001953 0.4421385816210791 0.007812 0.4392337954568403 0.031250 0.4278985729709260 0.125000 0.3865282566185451 0.500000 0.2653820441323137 1.000000 0.1684873483833459 1.250000 0.1360920003251323 1.500000 0.1107033002772792 1.875000 0.0821260199955304 2.000000 0.0745387819995946 2.125000 0.0677320343776128 3.000000 0.0356418086988119 4.000000 0.0179565899566183 5.000000 0.0094058737143575 6.000000 0.0050809356204299 7.000000 0.0028149565414210 10.000000 0.0005380869642256 15.000000 0.0000448217563801 20.000000 0.0000046890678427 40.000000 0.0000000020161545 agm_values_test(): agm_values() stores values of the arithmetic geometric mean function. A B AGM(A,B) 22.000000 96.000000 52.2746411987042379 83.000000 56.000000 68.8365300598585179 42.000000 7.000000 20.6593011967340097 26.000000 11.000000 17.6968548737436500 4.000000 63.000000 23.8670497217533004 6.000000 45.000000 20.7170159828059930 40.000000 75.000000 56.1278422556166845 80.000000 0.000000 0.0000000000000000 90.000000 35.000000 59.2695650812296364 9.000000 1.000000 3.9362355036495553 53.000000 53.000000 53.0000000000000000 1.000000 2.000000 1.4567910310469068 1.000000 4.000000 2.2430285802876027 1.000000 8.000000 3.6157561775973628 airy_ai_values_test(): airy_ai_values() stores values of the Airy function Ai(x). X Ai(X) 0.000000 0.3550280538878172 0.100000 0.3292031299435381 0.200000 0.3037031542863820 0.300000 0.2788064819550049 0.400000 0.2547423542956763 0.500000 0.2316936064808335 0.600000 0.2098000616663795 0.700000 0.1891624003981501 0.800000 0.1698463174443649 0.900000 0.1518868036405444 1.000000 0.1352924163128814 airy_ai_int_values_test(): airy_ai_int_values() stores values of the integral of the Airy Ai function. X FX -12.000000 -0.7522883891661012 -11.000000 -0.5734835018585489 -10.000000 -0.7656984031342129 -9.500000 -0.6518101550538247 -9.000000 -0.5588197489447188 -6.500000 -0.5690235287071681 -4.000000 -0.4780074964292617 -1.000000 -0.4656739834670686 -0.250000 -0.0967831409456180 -0.000977 -0.0003468304985704 0.000977 0.0003465836691793 0.007812 0.0027657581846051 0.500000 0.1459533049118572 1.000000 0.2363173419171098 4.000000 0.3328926453861221 4.500000 0.3331875912977942 6.000000 0.3333294517052385 8.000000 0.3333333172424836 10.000000 0.3333333332991690 12.000000 0.3333333333332938 airy_ai_prime_values_test(): airy_ai_prime_values() stores values of the derivative of the Airy Ai function. X FX 0.000000 -0.2588194037928068 0.100000 -0.2571304219075862 0.200000 -0.2524054702856195 0.300000 -0.2451463642190548 0.400000 -0.2358320344192082 0.500000 -0.2249105326646839 0.600000 -0.2127932593891585 0.700000 -0.1998511915822805 0.800000 -0.1864128638072717 0.900000 -0.1727638434616347 1.000000 -0.1591474412967932 airy_bi_values_test(): airy_bi_values() stores values of the Airy function Bi(x). X Bi(X) 0.000000 0.6149266274460007 0.100000 0.6598616901941892 0.200000 0.7054642029186612 0.300000 0.7524855850873156 0.400000 0.8017730000135972 0.500000 0.8542770431031556 0.600000 0.9110633416949405 0.700000 0.9733286558781659 0.800000 1.0424221712315609 0.900000 1.1198728131344471 1.000000 1.2074235949528711 airy_bi_int_values_test(): airy_bi_int_values() stores values of the integral of the Airy Bi function. X FX -12.000000 0.01766081903155463 -10.000000 -0.01504042480614002 -8.000000 0.01475644629322766 -7.500000 -0.1184730426484845 -7.000000 -0.06491674126616585 -6.500000 0.09726083246438104 -4.000000 0.05076005849528754 -1.000000 -0.3730050096342949 -0.250000 -0.1396298844266658 -0.001953 -0.00120017352667233 0.001953 0.001201883611789035 0.500000 0.3653384655095201 1.000000 0.8727691167380082 4.000000 48.21947526380343 8.000000 440065.2580490418 8.500000 1760815.39762283 9.000000 7377921.170522001 10.000000 147809803.1074067 12.000000 97037614223.61343 14.000000 116327376388098.8 airy_bi_prime_values_test(): airy_bi_prime_values() stores values of the derivative of the Airy Bi function. X FX 0.000000 0.4482883573538264 0.100000 0.4515126311496465 0.200000 0.4617892843621509 0.300000 0.4800490287524480 0.400000 0.5072816760506224 0.500000 0.5445725641405923 0.600000 0.5931444786342857 0.700000 0.6544059191721400 0.800000 0.7300069016152518 0.900000 0.8219038903072090 1.000000 0.9324359333927756 airy_cai_values_test(): airy_cai_values() stores values of the complex Airy function Ai(x). X.real X.imag Ai.real Ai.imag 1 0 0.1352924163128814 0 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 -0.08154602160771214 -1 0 0.5355608832923521 0 -0.809017 -0.587785 0.5983692170633874 0.08154602160771214 -0.309017 -0.951057 0.4763929771766866 0.3036484220291284 0.309017 -0.951057 0.2215404472324631 0.2588711788891803 0.809017 -0.587785 0.1433824486882056 0.1092193342707378 airy_cbi_values_test(): airy_cbi_values() stores values of the complex Airy function Bi(x). X.real X.imag Bi.real(X) Bi.imag(X) 1.000000 0.000000 1.2074235949528711 0 0.809017 0.587785 0.9127160108293936 0.3800456133135556 0.309017 0.951057 0.6824453575635721 0.3343047153635002 -0.309017 0.951057 0.5726265660086474 0.3988641086982559 -0.809017 0.587785 0.2511841251049547 0.3401447690712719 -1.000000 0.000000 0.1039973894969446 0 -0.809017 -0.587785 0.2511841251049547 -0.3401447690712719 -0.309017 -0.951057 0.5726265660086474 -0.3988641086982559 0.309017 -0.951057 0.6824453575635721 -0.3343047153635002 0.809017 -0.587785 0.9127160108293936 -0.3800456133135556 airy_gi_values_test(): airy_gi_values() stores values of the Airy function Gi(x). X Gi(X) -0.001953 0.2046830807004054 -0.125000 0.183746628325579 -1.000000 -0.1166722172960153 -4.000000 0.3146693490272956 -8.000000 -0.3708904072242626 -8.250000 -0.2529305977242402 -9.000000 0.289674106586927 -10.000000 -0.3464483649263409 -11.000000 0.2807603591387305 -13.000000 0.2181499450809486 0.001953 0.205266790008105 0.125000 0.2212369536378477 1.000000 0.2352184398104379 4.000000 0.08283430336376874 7.000000 0.04575738549098928 7.250000 0.04415001201460516 8.000000 0.03995113371950891 9.000000 0.03546770683394967 10.000000 0.03189600510067959 12.000000 0.02655689271351241 arccos_values_test(): arccos_values() stores values of the arc cosine function. X F(X) -0.100000 1.670963747956457 0.000000 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 1.000000 0 arccosh_values_test(): arccosh_values() stores values of the hyperbolic arc cosine function. X F(X) 1.000000 0 1.010000 0.1413037694856486 1.100000 0.4435682543851152 1.200000 0.6223625037147786 1.300000 0.7564329108569596 1.400000 0.8670147264905651 1.500000 0.9624236501192069 2.000000 1.316957896924817 3.000000 1.762747174039086 3.141593 1.811526272460853 4.000000 2.06343706889556 5.000000 2.292431669561178 10.000000 2.993222846126381 100.000000 5.298292365610485 1000.000000 7.600902209541989 arcsin_values_test(): arcsin_values() stores values of the arc sine function. X F(X) -0.100000 -0.1001674211615598 0.000000 0 0.100000 0.1001674211615598 0.200000 0.2013579207903308 0.300000 0.3046926540153975 0.400000 0.411516846067488 0.500000 0.5235987755982989 0.600000 0.6435011087932844 0.700000 0.7753974966107531 0.800000 0.9272952180016122 0.900000 1.119769514998634 1.000000 1.570796326794897 arcsinh_values_test(): arcsinh_values() stores values of the hyperbolic arc sine function. X F(X) -5.000000 -2.312438341272752 -1.000000 -0.881373587019543 0.000000 0 0.100000 0.09983407889920756 0.200000 0.1986901103492414 0.300000 0.2956730475634224 0.400000 0.3900353197707153 0.500000 0.4812118250596035 0.600000 0.5688248987322475 0.700000 0.6526665660823557 0.800000 0.7326682560454109 0.900000 0.8088669356527824 1.000000 0.881373587019543 2.000000 1.44363547517881 3.000000 1.818446459232067 4.000000 2.094712547261101 5.000000 2.312438341272752 10.000000 2.99822295029797 100.000000 5.298342365610589 1000.000000 7.600902709541988 arctan_values_test(): arctan_values() stores values of the arc tangent function. X F(X) 0.000000 0 0.250000 0.2449786631268641 0.333333 0.3217505543966422 0.500000 0.4636476090008061 1.000000 0.7853981633974483 2.000000 1.10714871779409 3.000000 1.249045772398254 4.000000 1.325817663668033 5.000000 1.373400766945016 10.000000 1.471127674303735 20.000000 1.520837931072954 arctan_int_values_test(): arctan_int_values() stores values of the arc tangent integral. X F(X) 0.001953 0.001953124172158848 -0.003906 -0.003906243377298071 0.007812 0.00781244701925765 0.015625 0.01562457618199653 -0.031250 -0.0312466103494854 0.062500 0.0624729113350144 0.125000 0.1247841971738965 -0.250000 -0.2483017509823069 0.500000 0.4872223582945224 1.000000 0.915965594177219 1.500000 1.27496944849438 -2.000000 -1.576015403446323 4.000000 2.425887841285909 8.000000 3.3911633326293 16.000000 4.417645091942219 -20.000000 -4.755671374954725 25.000000 5.096191215093411 30.000000 5.375917573571487 -50.000000 -6.164990478502749 100.000000 7.243784301308353 arctan2_values_test(): arctan2_values() stores values of the arc tangent function. X Y F(X,Y) 0.000000 -1.000000 -1.570796326794897 0.500000 -0.866025 -1.047197551196598 0.866025 -0.500000 -0.5235987755982989 1.000000 0.000000 0 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.047197551196598 0.000000 1.000000 1.570796326794897 -0.500000 0.866025 2.094395102393196 -0.866025 0.500000 2.617993877991494 -1.000000 0.000000 3.141592653589793 -0.866025 -0.500000 -2.617993877991494 -0.500000 -0.866025 -2.094395102393196 0.000000 -1.000000 -1.570796326794897 0.500000 -0.866025 -1.047197551196598 0.866025 -0.500000 -0.5235987755982989 1.000000 0.000000 0 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.047197551196598 0.000000 1.000000 1.570796326794897 arctanh_values_test(): arctanh_values() stores values of the hyperbolic arc tangent function. X F(X) -0.500000 -0.5493061443340549 0.000000 0 0.001000 0.001000000333333533 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 1.09861228866811 0.900000 1.47221948958322 0.990000 2.646652412362246 0.999000 3.8002011672502 0.999999 7.254328619262047 bei0_values_test(): bei0_values() stores values of the Kelvin BEI function. of order 0. X BEI(0,X) 0.000000 0 0.500000 0.06249321838219946 1.000000 0.2495660400366597 1.500000 0.5575600623030867 2.000000 0.9722916273066612 2.500000 1.457182044159804 3.000000 1.937586785266043 3.500000 2.283249966853915 4.000000 2.2926903226993 4.500000 1.686017203632139 5.000000 0.1160343815502004 bei1_values_test(): bei1_values() stores values of the Kelvin BEI function of order 1. X BEI(1,X) 0.000000 0 0.500000 0.1711951797170153 1.000000 0.3075566313755366 1.500000 0.3678649890020899 2.000000 0.2997754370020335 2.500000 0.03866844396595048 3.000000 -0.4874541770160708 3.500000 -1.344042373111174 4.000000 -2.563821688561078 4.500000 -4.105685408400878 5.000000 -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() stores values of the Kelvin BER function. of order 0. X BER(0,X) 0.000000 1 0.500000 0.9990234639908383 1.000000 0.9843817812130869 1.500000 0.9210721835462558 2.000000 0.7517341827138082 2.500000 0.3999684171295313 3.000000 -0.2213802495986939 3.500000 -1.193598179589928 4.000000 -2.56341655725858 4.500000 -4.299086551599756 5.000000 -6.230082478666358 ber1_values_test(): ber1_values() stores values of the Kelvin BER function of order 1. X BER(1,X) 0.000000 0 0.500000 -0.1822431237551121 1.000000 -0.3958682610197114 1.500000 -0.6648654179597691 2.000000 -0.9970776519264285 2.500000 -1.373096897645111 3.000000 -1.732644221128481 3.500000 -1.959644131289749 4.000000 -1.869248459031899 4.500000 -1.202821631480086 5.000000 0.3597766667766728 bernoulli_number_values_test(): bernoulli_number_values() returns values of the Bernoulli numbers. N bernoulli_number(N) 0 1 1 -0.5 2 0.166667 3 0 4 -0.0333333 6 -0.0238095 8 -0.0333333 10 0.0757576 20 -529.124 30 6.01581e+08 bernoulli_poly_values_test(): bernoulli_poly_values() stores values of the Bernoulli polynomials. N X FX 0 0.200000 1 1 0.200000 -0.3 2 0.200000 0.006666666666666667 3 0.200000 0.048 4 0.200000 -0.007733333333333333 5 0.200000 -0.02368 6 0.200000 0.00691352380952381 7 0.200000 0.0249088 8 0.200000 -0.01014997333333333 9 0.200000 -0.045278208 10 0.200000 0.02332631815757576 5 -0.500000 -0.3125 5 -0.400000 -0.11424 5 -0.300000 -0.01768 5 -0.200000 0.01568 5 -0.100000 0.01474 5 0.000000 0 5 0.100000 -0.01524 5 0.200000 -0.02368 5 0.300000 -0.02282 5 0.400000 -0.01376 5 0.500000 0 5 0.600000 0.01376 5 0.700000 0.02282 5 0.800000 0.02368 5 0.900000 0.01524 5 1.000000 0 bernstein_poly_01_values_test(): bernstein_poly_01_values() stores values of Bernstein polynomials. N K X F 0 0 0.250000 1 1 0 0.250000 0.75 1 1 0.250000 0.25 2 0 0.250000 0.5625 2 1 0.250000 0.375 2 2 0.250000 0.0625 3 0 0.250000 0.421875 3 1 0.250000 0.421875 3 2 0.250000 0.140625 3 3 0.250000 0.015625 4 0 0.250000 0.31640625 4 1 0.250000 0.421875 4 2 0.250000 0.2109375 4 3 0.250000 0.046875 4 4 0.250000 0.00390625 bessel_i0_values_test(): bessel_i0_values() stores values of the Bessel I function. of order 0. X I(0,X) 0.000000 1 0.200000 1.010025027795146 0.400000 1.040401782229341 0.600000 1.09204536431734 0.800000 1.166514922869803 1.000000 1.266065877752008 1.200000 1.393725584134064 1.400000 1.553395099731217 1.600000 1.749980639738909 1.800000 1.989559356618051 2.000000 2.279585302336067 2.500000 3.289839144050123 3.000000 4.880792585865024 3.500000 7.37820343222548 4.000000 11.30192195213633 4.500000 17.48117185560928 5.000000 27.23987182360445 6.000000 67.23440697647798 8.000000 427.5641157218048 10.000000 2815.716628466254 bessel_i0_int_values_test(): bessel_i0_int_values() stores values of the Bessel I integral. of order 0. X int_i(0,X) 0.001953 0.001953125620881805 -0.003906 -0.003906254967056573 0.062500 0.06252034803254657 0.125000 0.1251628558136697 -0.500000 -0.5105148087974031 1.000000 1.08652109702359 2.000000 2.775001905428253 -4.000000 -13.77520886803972 8.000000 464.2437205810611 18.000000 6411186.765802158 -18.500000 -10414860.80317586 20.000000 44758598.91385575 -21.000000 -118529853.1155829 22.000000 314300782.2071599 -23.000000 -834402129.0079432 24.000000 2217536757.90743 25.000000 5899173184.280364 -27.000000 -41857073244.69152 30.000000 795538858184.7236 40.000000 1.50897150827192e+16 bessel_i0_spherical_values_test(): bessel_i0_spherical_values: values of the spherical Bessel I function. of order 0. X Spherical I(0,X) 0.100000 1.00166750019844 0.200000 1.00668001270547 0.400000 1.026880814507039 0.600000 1.061089303580402 0.800000 1.110132477734529 1.000000 1.175201193643801 1.200000 1.257884462843477 1.400000 1.360215358179667 1.600000 1.484729970750144 1.800000 1.634541271164267 2.000000 1.813430203923509 2.200000 2.025956895698133 2.400000 2.277595505698373 2.600000 2.574897010920645 2.800000 2.925685126512827 3.000000 3.339291642469967 3.200000 3.826838748926716 3.400000 4.401577467270101 3.600000 5.079293155726485 3.800000 5.878791279137455 4.000000 6.822479299281938 bessel_i1_values_test(): bessel_i1_values() stores values of the Bessel I function. of order 1. X I(1,X) 0.000000 0 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.000000 0.565159103992485 1.200000 0.7146779415526431 1.400000 0.8860919814143274 1.600000 1.08481063512988 1.800000 1.317167230391899 2.000000 1.590636854637329 2.500000 2.516716245288698 3.000000 3.953370217402609 3.500000 6.205834922258365 4.000000 9.759465153704451 4.500000 15.38922275373592 5.000000 24.33564214245053 6.000000 61.34193677764024 8.000000 399.8731367825601 10.000000 2670.988303701255 bessel_i1_spherical_values_test(): bessel_i1_spherical_values() stores values of the spherical Bessel I function. of order 1. X Spherical I(1,X) 0.100000 0.03336667857363341 0.200000 0.06693371456802955 0.400000 0.1354788933285401 0.600000 0.2072931911031093 0.800000 0.2841280857128948 1.000000 0.3678794411714423 1.200000 0.4606425870674146 1.400000 0.5647736480096238 1.600000 0.6829590627779635 1.800000 0.8182955028627777 2.000000 0.9743827435800611 2.200000 1.155432469636406 2.400000 1.366396525527973 2.600000 1.613118767572064 2.800000 1.902515460838681 3.000000 2.242790117769266 3.200000 2.643689828630357 3.400000 3.116811526884873 3.600000 3.675968313148932 3.800000 4.337627987747642 4.000000 5.121438384183637 bessel_in_values_test(): bessel_in_values() stores values of the Bessel I function. of order NU. NU X I(NU,X) 2 0.200000 0.005016687513894678 2 1.000000 0.1357476697670383 2 2.000000 0.6889484476987382 2 2.500000 1.276466147819164 2 3.000000 2.245212440929951 2 5.000000 17.50561496662424 2 10.000000 2281.518967726004 2 20.000000 39312785.22104076 3 1.000000 0.0221684249243319 3 2.000000 0.2127399592398527 3 5.000000 10.33115016915114 3 10.000000 1758.380716610853 3 50.000000 2.677764138883941e+20 5 1.000000 0.0002714631559569719 5 2.000000 0.009825679323131702 5 5.000000 2.157974547322546 5 10.000000 777.18828640326 5 50.000000 2.278548307911282e+20 10 1.000000 2.752948039836874e-10 10 2.000000 3.016963879350684e-07 10 5.000000 0.004580044419176051 10 10.000000 21.89170616372337 10 50.000000 1.071597159477637e+20 20 1.000000 3.96683598581902e-25 20 2.000000 4.310560576109548e-19 20 5.000000 5.024239357971806e-11 20 10.000000 0.0001250799735644948 20 50.000000 5.442008402752998e+18 bessel_ix_values_test(): bessel_ix_values() stores values of the Bessel I function. of real order NU. NU X I(NU,X) 0.500000 0.200000 0.3592084175833614 0.500000 1.000000 0.9376748882454876 0.500000 2.000000 2.046236863089055 0.500000 2.500000 3.053093538196718 0.500000 3.000000 4.614822903407601 0.500000 5.000000 26.47754749755907 0.500000 10.000000 2778.784603874571 0.500000 20.000000 43279746.27242893 1.500000 1.000000 0.2935253263474798 1.500000 2.000000 1.09947318863311 1.500000 5.000000 21.18444226479414 1.500000 10.000000 2500.906154942118 1.500000 50.000000 2.866653715931464e+20 2.500000 1.000000 0.05709890920304825 2.500000 2.000000 0.3970270801393905 2.500000 5.000000 13.76688213868258 2.500000 10.000000 2028.512757391936 2.500000 50.000000 2.753157630035402e+20 1.250000 1.000000 0.4139416015642352 1.250000 2.000000 1.340196758982897 1.250000 5.000000 22.8571551036467 1.250000 10.000000 2593.006763432002 1.250000 50.000000 2.886630075077766e+20 2.750000 1.000000 0.03590910483251082 2.750000 2.000000 0.2931108636266483 2.750000 5.000000 11.99397010023068 2.750000 10.000000 1894.575731562383 2.750000 50.000000 2.716911375760483e+20 bessel_j_spherical_values_test(): bessel_j_spherical_values() stores values of the spherical Bessel J function. of order N. N X Spherical J(N,X) 0 0.905000 0.8689780717709105 1 0.905000 0.2776712616989048 2 0.905000 0.05147914933043151 3 0.905000 0.006743927971987495 4 0.905000 0.0006838294584220406 5 0.905000 5.658597917091951e-05 6 0.905000 3.955923765931341e-06 7 0.905000 2.394450910776484e-07 8 0.905000 1.277940110150618e-08 9 0.905000 6.099572379372921e-10 10 0.905000 2.633096568558721e-11 0 10.000000 -0.05440211108893698 1 10.000000 0.07846694179875155 2 10.000000 0.07794219362856245 3 10.000000 -0.03949584498447032 4 10.000000 -0.1055892851176917 5 10.000000 -0.05553451162145218 6 10.000000 0.04450132233409427 7 10.000000 0.1133862306557747 8 10.000000 0.1255780236495678 9 10.000000 0.1000964095484906 10 10.000000 0.06460515449256427 bessel_j0_values_test(): bessel_j0_values() stores values of the Bessel J function. of order 0. X J(0,X) -5.000000 -0.1775967713143383 -4.000000 -0.3971498098638474 -3.000000 -0.2600519549019334 -2.000000 0.2238907791412357 -1.000000 0.7651976865579666 0.000000 1 1.000000 0.7651976865579666 2.000000 0.2238907791412357 3.000000 -0.2600519549019334 4.000000 -0.3971498098638474 5.000000 -0.1775967713143383 6.000000 0.1506452572509969 7.000000 0.3000792705195556 8.000000 0.1716508071375539 9.000000 -0.09033361118287613 10.000000 -0.2459357644513483 11.000000 -0.1711903004071961 12.000000 0.04768931079683354 13.000000 0.2069261023770678 14.000000 0.1710734761104587 15.000000 -0.01422447282678077 bessel_j0_int_values_test(): bessel_j0_int_values() stores values of the Bessel J integral. of order 0. X int_j(0,X) 0.000977 0.0009765624223897882 0.003906 0.003906245032949111 -0.062500 -0.06247965792791793 0.125000 0.1248373349212048 -0.500000 -0.4896805066460451 1.000000 0.9197304100897602 -2.000000 -1.425770293197027 4.000000 1.024734159460607 -8.000000 -1.21074683483045 16.000000 1.100865203273619 -16.500000 -1.006033482990413 18.000000 0.8133057266248596 -20.000000 -1.058378821421128 25.000000 0.8710149211654588 -30.000000 -0.8842490888254749 40.000000 1.125776150359991 -50.000000 -0.9014121225818346 75.000000 0.9144134436964779 -80.000000 -0.944822819383344 100.000000 0.9226625569601661 bessel_j0_spherical_values_test(): bessel_j0_spherical_values() stores values of the spherical Bessel J function. of order 0. X Spherical J(0,X) 0.100000 0.9983341664682815 0.200000 0.9933466539753061 0.400000 0.9735458557716262 0.600000 0.9410707889917256 0.800000 0.8966951136244035 1.000000 0.8414709848078965 1.200000 0.7766992383060221 1.400000 0.7038926642774715 1.600000 0.6247335019009407 1.800000 0.5410264615989973 2.000000 0.4546487134128408 2.200000 0.367498365372541 2.400000 0.2814429918963129 2.600000 0.1982697583928709 2.800000 0.1196386250556803 3.000000 0.04704000268662241 3.200000 -0.01824191982111872 3.400000 -0.0751591476549504 3.600000 -0.1229223453596812 3.800000 -0.1610152344586103 4.000000 -0.1892006238269821 bessel_j0_zero_values_test(): bessel_j0_zero_values stores zeros of the Bessel J0 function. K X(K) 1 2.404825557695773 2 5.520078110286311 3 8.653727912911013 4 11.79153443901428 5 14.93091770848779 6 18.07106396791092 7 21.21163662987926 8 24.3524715307493 9 27.49347913204025 10 30.63460646843198 11 33.77582021357357 12 36.91709835366404 13 40.05842576462824 14 43.19979171317673 15 46.34118837166181 16 49.48260989739781 17 52.624051841115 18 55.76551075501998 19 58.90698392608094 20 62.04846919022717 21 65.18996480020687 22 68.3314693298568 23 71.47298160359374 24 74.61450064370183 25 77.75602563038805 26 80.89755587113763 27 84.0390907769382 28 87.18062984364116 29 90.32217263721049 30 93.46371878194478 bessel_j1_values_test(): bessel_j1_values() stores values of the Bessel J function. of order 1. X J(1,X) -5.000000 0.3275791375914652 -4.000000 0.06604332802354913 -3.000000 -0.3390589585259365 -2.000000 -0.5767248077568734 -1.000000 -0.4400505857449335 0.000000 0 1.000000 0.4400505857449335 2.000000 0.5767248077568734 3.000000 0.3390589585259365 4.000000 -0.06604332802354913 5.000000 -0.3275791375914652 6.000000 -0.2766838581275656 7.000000 -0.004682823482345833 8.000000 0.2346363468539146 9.000000 0.2453117865733253 10.000000 0.04347274616886144 11.000000 -0.1767852989567215 12.000000 -0.2234471044906276 13.000000 -0.07031805212177837 14.000000 0.1333751546987933 15.000000 0.2051040386135228 bessel_j1_spherical_values_test(): bessel_j1_spherical_values() stores values of the spherical Bessel J function. of order 1. X Spherical J(1,X) 0.100000 0.03330001190255757 0.200000 0.06640038067032222 0.400000 0.1312121544218529 0.600000 0.1928919568034122 0.800000 0.2499855053465475 1.000000 0.3011686789397568 1.200000 0.3452845698577903 1.400000 0.3813753724123076 1.600000 0.4087081401263934 1.800000 0.4267936423844913 2.000000 0.4353977749799916 2.200000 0.4345452193763121 2.400000 0.4245152947656493 2.600000 0.4058301968314685 2.800000 0.3792360591872637 3.000000 0.345677499762356 3.200000 0.3062665174917607 3.400000 0.2622467779189737 3.600000 0.2149544641595738 3.800000 0.165776967751528 4.000000 0.1161107492591575 bessel_jn_values_test(): bessel_jn_values() stores values of the Bessel J function. of order NU. NU X J(NU,X) 2 1.000000 0.1149034849319005 2 2.000000 0.3528340286156377 2 5.000000 0.04656511627775222 2 10.000000 0.2546303136851206 2 50.000000 -0.05971280079425882 5 1.000000 0.0002497577302112344 5 2.000000 0.007039629755871685 5 5.000000 0.2611405461201701 5 10.000000 -0.2340615281867936 5 50.000000 -0.08140024769656964 10 1.000000 2.630615123687453e-10 10 2.000000 2.515386282716737e-07 10 5.000000 0.001467802647310474 10 10.000000 0.2074861066333589 10 50.000000 -0.1138478491494694 20 1.000000 3.873503008524658e-25 20 2.000000 3.918972805090754e-19 20 5.000000 2.770330052128942e-11 20 10.000000 1.15133692478134e-05 20 50.000000 -0.1167043527595797 bessel_jx_values_test(): bessel_jx_values() stores values of the Bessel J function. of real order NU. NU X J(NU,X) 0.500000 0.200000 0.3544507442114011 0.500000 1.000000 0.6713967071418031 0.500000 2.000000 0.5130161365618278 0.500000 2.500000 0.3020049060623657 0.500000 3.000000 0.06500818287737578 0.500000 5.000000 -0.3421679847981618 0.500000 10.000000 -0.1372637357550505 0.500000 20.000000 0.1628807638550299 1.500000 1.000000 0.240297839123427 1.500000 2.000000 0.4912937786871623 1.500000 5.000000 -0.1696513061447408 1.500000 10.000000 0.1979824927558931 1.500000 50.000000 -0.109476872988318 2.500000 1.000000 0.04949681022847794 2.500000 2.000000 0.2239245314689158 2.500000 5.000000 0.2403772011113174 2.500000 10.000000 0.1966584835818184 2.500000 50.000000 0.02303721950962553 1.250000 1.000000 0.3314145508558904 1.250000 2.000000 0.546173424040284 1.250000 5.000000 -0.2616584152094124 1.250000 10.000000 0.1296035513791289 1.250000 50.000000 -0.1117432171933552 2.750000 1.000000 0.03142623570527935 2.750000 2.000000 0.1717922192746527 2.750000 5.000000 0.3126634069544786 2.750000 10.000000 0.1340289119304364 2.750000 50.000000 0.06235967135106445 bessel_k0_values_test(): bessel_k0_values() stores values of the Bessel K function. of order 0. X K(0,X) 0.100000 2.427069024702017 0.200000 1.752703855528146 0.400000 1.114529134524434 0.600000 0.7775220919047293 0.800000 0.5653471052658957 1.000000 0.4210244382407083 1.200000 0.3185082202865936 1.400000 0.2436550611815419 1.600000 0.1879547519693323 1.800000 0.145931400489828 2.000000 0.1138938727495334 2.500000 0.06234755320036619 3.000000 0.03473950438627925 3.500000 0.01959889717036849 4.000000 0.01115967608585302 4.500000 0.006399857243233975 5.000000 0.003691098334042594 6.000000 0.001243994328013123 8.000000 0.0001464707052228154 10.000000 1.778006231616765e-05 bessel_k0_int_values_test(): bessel_k0_int_values() stores values of the Bessel K integral. of order 0. X int_k(0,X) 0.000977 0.007858792956346679 0.003906 0.02601999161733058 0.062500 0.2431184223754117 0.125000 0.3999963375048051 0.500000 0.9271025209311491 1.000000 1.242509848623778 2.000000 1.473675734316829 4.000000 1.560649570605174 5.000000 1.567387390728366 6.000000 1.569634553269374 6.500000 1.570115344325079 8.000000 1.570657485289444 10.000000 1.570779311615979 12.000000 1.570794206646577 15.000000 1.570796231546919 20.000000 1.570796326234015 30.000000 1.570796326794876 50.000000 1.570796326794897 80.000000 1.570796326794897 100.000000 1.570796326794897 bessel_k1_values_test(): bessel_k1_values() stores values of the Bessel K function. of order 1. X K(1,X) 0.100000 9.853844780870606 0.200000 4.775972543220472 0.400000 2.184354424732687 0.600000 1.302834939763502 0.800000 0.8617816344721803 1.000000 0.6019072301972346 1.200000 0.434592391060715 1.400000 0.3208359022298758 1.600000 0.2406339113576119 1.800000 0.182623099801747 2.000000 0.1398658818165224 2.500000 0.07389081634774707 3.000000 0.04015643112819418 3.500000 0.02223939292592383 4.000000 0.01248349888726843 4.500000 0.00707809490896809 5.000000 0.004044613445452164 6.000000 0.001343919717735509 8.000000 0.0001553692118050011 10.000000 1.864877345382558e-05 bessel_kn_values_test(): bessel_kn_values() stores values of the Bessel K function. of order NU. NU X K(NU,X) 2 0.200000 49.51242928773287 2 1.000000 1.624838898635177 2 2.000000 0.2537597545660559 2 2.500000 0.1214602062785638 2 3.000000 0.06151045847174204 2 5.000000 0.00530894371222346 2 10.000000 2.150981700693277e-05 2 20.000000 6.329543612292228e-10 3 1.000000 7.101262824737945 3 2.000000 0.6473853909486342 3 5.000000 0.008291768415230933 3 10.000000 2.725270025659869e-05 3 50.000000 3.727936773826211e-23 5 1.000000 360.9605896012407 5 2.000000 9.431049100596468 5 5.000000 0.03270627371203186 5 10.000000 5.754184998531228e-05 5 50.000000 4.367182254100986e-23 10 1.000000 180713289.9010295 10 2.000000 162482.4039795591 10 5.000000 9.75856282917781 10 10.000000 0.00161425530039067 10 50.000000 9.150988209987996e-23 20 1.000000 6.294369360424535e+22 20 2.000000 5.770856852700241e+16 20 5.000000 482700052.0621485 20 10.000000 178.7442782077055 20 50.000000 1.706148379722035e-21 bessel_kx_values_test(): bessel_kx_values() stores values of the Bessel K function. of real order NU. NU X K(NU,X) 0.500000 0.200000 2.294489339798475 0.500000 1.000000 0.4610685044478946 0.500000 2.000000 0.1199377719680614 0.500000 2.500000 0.06506594315400999 0.500000 3.000000 0.03602598513176459 0.500000 5.000000 0.003776613374642883 0.500000 10.000000 1.799347809370518e-05 0.500000 20.000000 5.776373974707445e-10 1.500000 1.000000 0.9221370088957891 1.500000 2.000000 0.1799066579520922 1.500000 5.000000 0.004531936049571459 1.500000 10.000000 1.97928259030757e-05 1.500000 50.000000 3.486992497366216e-23 2.500000 1.000000 3.227479531135262 2.500000 2.000000 0.3897977588961997 2.500000 5.000000 0.006495775004385758 2.500000 10.000000 2.393132586462789e-05 2.500000 50.000000 3.627839645299048e-23 1.250000 1.000000 0.7311451879202114 1.250000 2.000000 0.1567475478393932 1.250000 5.000000 0.004257389528177461 1.250000 10.000000 1.915541065869563e-05 1.250000 50.000000 3.463337593569306e-23 2.750000 1.000000 4.731184839919541 2.750000 2.000000 0.4976876225514758 2.750000 5.000000 0.007300864610941163 2.750000 10.000000 2.546421294106458e-05 2.750000 50.000000 3.675275677913656e-23 bessel_y0_values_test(): bessel_y0_values() stores values of the Bessel Y function. of order 0. X Y(0,X) 0.100000 -1.534238651350367 1.000000 0.08825696421567696 2.000000 0.5103756726497451 3.000000 0.3768500100127904 4.000000 -0.01694073932506499 5.000000 -0.3085176252490338 6.000000 -0.2881946839815792 7.000000 -0.02594974396720926 8.000000 0.2235214893875662 9.000000 0.2499366982850247 10.000000 0.05567116728359939 11.000000 -0.1688473238920795 12.000000 -0.2252373126343614 13.000000 -0.07820786452787591 14.000000 0.1271925685821837 15.000000 0.2054642960389183 bessel_y0_int_values_test(): bessel_y0_int_values() stores values of the Bessel Y integral. of order 0. X int_y(0,X) 0.001953 -0.009144264286017211 0.007812 -0.02968204739039759 0.125000 -0.2539143127658539 0.500000 -0.5617954559146403 1.000000 -0.6370693766074231 2.000000 -0.2821928500851009 4.000000 0.3836696478531256 6.000000 -0.1259506128579893 10.000000 0.2412903183226668 16.000000 0.1713806975762704 16.250000 0.1895814262713408 17.000000 0.1720384613644971 20.000000 -0.1682159767721503 25.000000 -0.09360792735142899 30.000000 0.08822971194803665 40.000000 -0.008932466273627416 50.000000 -0.05481407100006349 70.000000 -0.09495824600346638 100.000000 -0.01959806485340497 125.000000 -0.008308477235715477 bessel_y0_spherical_values_test(): bessel_y0_spherical_values() stores values of the spherical Bessel Y function. of order 0. X Spherical Y(0,X) 0.100000 -9.950041652780259 0.200000 -4.900332889206208 0.400000 -2.302652485007213 0.600000 -1.375559358182797 0.800000 -0.8708833866839568 1.000000 -0.5403023058681397 1.200000 -0.301964795397228 1.400000 -0.1214051020716007 1.600000 0.01824970143830545 1.800000 0.1262233859406039 2.000000 0.2080734182735712 2.200000 0.267500507843339 2.400000 0.307247381475519 2.600000 0.3295725974495951 2.800000 0.3365079788102351 3.000000 0.3299974988668152 3.200000 0.3119671174358603 3.400000 0.2843524095821944 3.600000 0.2490995600928186 3.800000 0.2081493978722149 4.000000 0.163410905215903 bessel_y0_zero_values_test(): bessel_y0_zero_values stores zeros of the Bessel Y0 function. K X(K) 1 0.8935769662791675 2 3.957678419314858 3 7.086051060301773 4 10.22234504349642 5 13.36109747387276 6 16.50092244152809 7 19.64130970088794 8 22.78202804729156 9 25.92295765318092 10 29.0640302527284 11 32.20520411649328 12 35.34645230521432 13 38.48775665308154 14 41.62910446621381 15 44.77048660722199 16 47.91189633151648 17 51.05332855236236 18 54.19477936108705 19 57.33624570476628 20 60.47772516422348 21 63.61921579772038 22 66.76071602872965 23 69.9022245639385 24 73.04374033239208 25 76.18526243968061 26 79.326790133004 27 82.46832277421549 28 85.60985981879671 29 88.75140079929514 30 91.89294531215718 31 95.03449300717121 32 98.17604357893667 bessel_y1_values_test(): bessel_y1_values() stores values of the Bessel Y function. of order 1. X Y(1,X) 0.100000 -6.458951094702027 1.000000 -0.7812128213002887 2.000000 -0.1070324315409375 3.000000 0.3246744247918 4.000000 0.3979257105571 5.000000 0.1478631433912268 6.000000 -0.1750103443003983 7.000000 -0.3026672370241849 8.000000 -0.1580604617312475 9.000000 0.1043145751967159 10.000000 0.2490154242069539 11.000000 0.1637055374149429 12.000000 -0.05709921826089652 13.000000 -0.2100814084206935 14.000000 -0.1666448418561723 15.000000 0.02107362803687351 bessel_y1_spherical_values_test(): bessel_y1_spherical_values() stores values of the spherical Bessel Y function of order 1. X Spherical Y(1,X) 0.100000 -100.4987506942709 0.200000 -25.49501110000635 0.400000 -6.730177068289658 0.600000 -3.233669719296388 0.800000 -1.985299346979349 1.000000 -1.381773290676036 1.200000 -1.028336567803712 1.400000 -0.7906105943286149 1.600000 -0.6133274385019998 1.800000 -0.4709023582986618 2.000000 -0.3506120042760553 2.200000 -0.2459072254437506 2.400000 -0.1534232496148467 2.600000 -0.07151106706610352 2.800000 0.0005427959479750482 3.000000 0.06295916360231597 3.200000 0.1157316440198251 3.400000 0.1587922092967723 3.600000 0.1921166676076864 3.800000 0.2157913917934037 4.000000 0.2300533501309578 bessel_yn_values_test(): bessel_yn_values() stores values of the Bessel Y function. of order NU. NU X Y(NU,X) 2 1.000000 -1.650682606816254 2 2.000000 -0.6174081041906827 2 5.000000 0.3676628826055245 2 10.000000 -0.005868082442208615 2 50.000000 0.09579316872759649 5 1.000000 -260.4058666258122 5 2.000000 -9.935989128481975 5 5.000000 -0.4536948224911019 5 10.000000 0.1354030476893623 5 50.000000 -0.07854841391308165 10 1.000000 -121618014.2786892 10 2.000000 -129184.5422080393 10 5.000000 -25.1291100956101 10 10.000000 -0.3598141521834027 10 50.000000 0.005723897182053514 20 1.000000 -4.113970314835505e+22 20 2.000000 -4.081651388998367e+16 20 5.000000 -593396529.6914321 20 10.000000 -1597.483848269626 20 50.000000 0.01644263394811578 bessel_yx_values_test(): bessel_yx_values() stores values of the Bessel Y function. of real order NU. NU X Y(NU,X) 0.500000 0.200000 -1.748560416961876 0.500000 1.000000 -0.4310988680183761 0.500000 2.000000 0.2347857104062485 0.500000 2.500000 0.4042783022390569 0.500000 3.000000 0.4560488207946332 0.500000 5.000000 -0.1012177091851084 0.500000 10.000000 0.2117088663313982 0.500000 20.000000 -0.07280690478506185 1.500000 1.000000 -1.102495575160179 1.500000 2.000000 -0.3956232813587035 1.500000 5.000000 0.3219244429611401 1.500000 10.000000 0.1584346223881903 1.500000 50.000000 0.02742813676191382 2.500000 1.000000 -2.876387857462161 2.500000 2.000000 -0.8282206324443037 2.500000 5.000000 0.2943723749617925 2.500000 10.000000 -0.1641784796149411 2.500000 50.000000 0.1105304445562544 1.250000 1.000000 -0.9319659251969881 1.250000 2.000000 -0.2609445010948933 1.250000 5.000000 0.2492796362185881 1.250000 10.000000 0.2174410301416733 1.250000 50.000000 -0.01578576650557229 2.750000 1.000000 -4.023453301501028 2.750000 2.000000 -0.9588998694752389 2.750000 5.000000 0.2264260361047367 2.750000 10.000000 -0.219361773656676 2.750000 50.000000 0.09413988344515077 beta_values_test(): beta_values() stores values of the BETA function. X Y BETA(X,Y) 0.200000 1.000000 5 0.400000 1.000000 2.5 0.600000 1.000000 1.666666666666667 0.800000 1.000000 1.25 1.000000 0.200000 5 1.000000 0.400000 2.5 1.000000 1.000000 1 2.000000 2.000000 0.1666666666666667 3.000000 3.000000 0.03333333333333333 4.000000 4.000000 0.007142857142857143 5.000000 5.000000 0.001587301587301587 6.000000 2.000000 0.02380952380952381 6.000000 3.000000 0.005952380952380952 6.000000 4.000000 0.001984126984126984 6.000000 5.000000 0.0007936507936507937 6.000000 6.000000 0.0003607503607503608 7.000000 7.000000 8.325008325008325e-05 beta_cdf_values_test(): beta_cdf_values() stores values of the BETA function. A B X beta_cdf(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_inc_values_test(): beta_inc_values() stores values of the BETA function. A B X beta_inc(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_log_values_test(): beta_log_values() stores values of the Log(BETA) function. X Y Log(BETA(X,Y)) 0.200000 1.000000 1.6094379124341 0.400000 1.000000 0.9162907318741551 0.600000 1.000000 0.5108256237659907 0.800000 1.000000 0.2231435513142098 1.000000 0.200000 1.6094379124341 1.000000 0.400000 0.9162907318741551 1.000000 1.000000 0 2.000000 2.000000 -1.791759469228055 3.000000 3.000000 -3.401197381662155 4.000000 4.000000 -4.941642422609304 5.000000 5.000000 -6.445719819385578 6.000000 2.000000 -3.737669618283368 6.000000 3.000000 -5.123963979403259 6.000000 4.000000 -6.222576268071369 6.000000 5.000000 -7.138866999945524 6.000000 6.000000 -7.927324360309794 7.000000 7.000000 -9.39366142910322 beta_noncentral_cdf_values_test(): beta_noncentral_cdf_values() stores values of the noncentral BETA CDF. A B LAMDA X beta_noncentral_cdf(A,B,LAMDA,X) 5.000000 5.000000 54.000000 0.864000 0.4563021 5.000000 5.000000 140.000000 0.900000 0.1041337 5.000000 5.000000 170.000000 0.956000 0.6022353 10.000000 10.000000 54.000000 0.868600 0.918777 10.000000 10.000000 140.000000 0.900000 0.6008106 10.000000 10.000000 250.000000 0.900000 0.090285 20.000000 20.000000 54.000000 0.878700 0.9998655 20.000000 20.000000 140.000000 0.900000 0.9925997 20.000000 20.000000 250.000000 0.922000 0.9641111999999999 10.000000 20.000000 150.000000 0.868000 0.9376626573 10.000000 10.000000 120.000000 0.900000 0.7306817858 15.000000 5.000000 80.000000 0.880000 0.1604256918 20.000000 10.000000 110.000000 0.850000 0.1867485313 20.000000 30.000000 65.000000 0.660000 0.6559386874000001 20.000000 50.000000 130.000000 0.720000 0.9796881486 30.000000 20.000000 80.000000 0.720000 0.1162386423 30.000000 40.000000 130.000000 0.800000 0.9930430054 10.000000 5.000000 20.000000 0.644000 0.0506899273 10.000000 10.000000 54.000000 0.700000 0.1030959706 10.000000 30.000000 80.000000 0.780000 0.9978417832000001 15.000000 20.000000 120.000000 0.760000 0.2555552369 10.000000 5.000000 55.000000 0.795000 0.0668307064 12.000000 17.000000 64.000000 0.560000 0.0113601067 30.000000 30.000000 140.000000 0.800000 0.7813366615 35.000000 30.000000 20.000000 0.670000 0.8867126477 beta_pdf_values_test(): beta_pdf_values() stores values of the BETA function. ALPHA BETA X PDF() 1.09209 4.78159 0.866722 0.002826137156803199 2.80848 2.07654 0.0460776 0.04208950342768649 1.28789 0.549784 0.0221162 0.2184064957817208 3.16983 0.308636 0.458254 0.1335142301445414 2.00653 3.77337 0.832083 0.1070571849830009 0.00919186 4.48752 0.352059 0.005796394377470491 0.472724 0.0680845 0.898529 0.5518796772414584 4.20424 0.61552 -0.0169242 0 1.30151 4.56242 0.0971888 2.87907465409348 1.75814 4.11444 0.262167 2.126992854611924 binomial_values_test(): binomial_values() stores values of the BINOMIAL function. A B BINOMIAL(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() stores values of the BINOMIAL CDF. A B X binomial_cdf(A,B,X) 2.000000 0.050000 0 0.9025 2.000000 0.050000 1 0.9975000000000001 2.000000 0.050000 2 1 2.000000 0.500000 0 0.25 2.000000 0.500000 1 0.75 4.000000 0.250000 0 0.31640625 4.000000 0.250000 1 0.73828125 4.000000 0.250000 2 0.94921875 4.000000 0.250000 3 0.99609375 10.000000 0.050000 4 0.9999363101685547 10.000000 0.100000 4 0.9983650626 10.000000 0.150000 4 0.9901259090013672 10.000000 0.200000 4 0.9672065023999999 10.000000 0.250000 4 0.9218730926513672 10.000000 0.300000 4 0.8497316673999999 10.000000 0.400000 4 0.6331032576 10.000000 0.500000 4 0.376953125 binomial_pdf_values_test(): binomial_pdf_values() stores values of the BINOMIAL PDF. A B X binomial_pdf(A,B,X) 5 0.8295092339327006 5 0.3927408939646697 12 0.06611873491603133 5 0.0006199968732461383 6 0.0438289977791071 0 0.764211224733124 13 0.4495389603071763 0 0.0004260353334364943 9 0.7972869541062562 7 0.302948289145794 1 0.3507523379805466 1 0.3507523379805466 2 0.8590968552798568 0 0.01985369619202562 17 0.007512364073964213 2 0.006854388879646552 6 0.1136640464424993 6 2.156446446382985e-06 8 0.2671322702601793 7 0.0005691150511772053 bivariate_normal_cdf_values_test(): bivariate_normal_cdf_values() stores values of the bivariate normal CDF. X Y R bivariate_normal_cdf(X,Y,R) -2.000000 1.000000 0.500000 0.02260327218569867 -1.000000 1.000000 0.500000 0.15487295185841 0.000000 1.000000 0.500000 0.4687428083352184 1.000000 1.000000 0.500000 0.7452035868929476 2.000000 1.000000 0.500000 0.8318608306874188 3.000000 1.000000 0.500000 0.8410314261134202 -0.200000 0.500000 -0.900000 0.1377019384919464 -0.200000 0.500000 -0.800000 0.162174950173903 -0.200000 0.500000 -0.700000 0.1827411243233119 -0.200000 0.500000 -0.600000 0.2010067421506235 -0.200000 0.500000 -0.500000 0.217775115526529 -0.200000 0.500000 -0.400000 0.2335088436446962 -0.200000 0.500000 -0.300000 0.2485057781834286 -0.200000 0.500000 -0.200000 0.2629747825154868 -0.200000 0.500000 -0.100000 0.2770729823404738 -0.200000 0.500000 0.000000 0.2909261168683812 -0.200000 0.500000 0.100000 0.3046406378726738 -0.200000 0.500000 0.200000 0.3183113449213638 -0.200000 0.500000 0.300000 0.3320262544108028 -0.200000 0.500000 0.400000 0.3458686754647614 -0.200000 0.500000 0.500000 0.3599150462310668 -0.200000 0.500000 0.600000 0.3742210899871168 -0.200000 0.500000 0.700000 0.388770640528232 -0.200000 0.500000 0.800000 0.4032765198361344 -0.200000 0.500000 0.900000 0.4162100291953678 1.000000 0.500000 0.673000 0.6508271498838664 2.000000 1.000000 0.500000 0.8318608306874188 0.000000 0.000000 -1.000000 0 0.000000 0.000000 -0.500000 0.166666666653997 0.000000 0.000000 0.000000 0.25 0.000000 0.000000 0.500000 0.3333333333328906 0.000000 0.000000 1.000000 0.5 1.000000 1.000000 0.500000 0.7452035868929476 1.000000 -1.000000 0.500000 0.15487295185841 -1.000000 1.000000 0.500000 0.15487295185841 -1.000000 -1.000000 0.500000 0.06251409470431653 1.000000 1.000000 0.500000 0.7452035868929476 1.000000 -1.000000 0.500000 0.15487295185841 -1.000000 1.000000 0.500000 0.15487295185841 -1.000000 -1.000000 0.500000 0.06251409470431653 0.707107 0.707107 0.500000 0.6337020457912916 c8_log_values_test(): c8_log_values() stores values of the complex logarithm function. Z.real Z.imag FZ.real FZ.imag -2 -2 1.039720770839918 -2.356194490192345 -2 1 0.80471895621705 2.677945044588987 -1 -1 0.346573590279973 -2.356194490192345 -1 0 0 3.141592653589793 0 -2 0.693147180559945 -1.570796326794897 0 -1 0 -1.570796326794897 0 1 0 1.570796326794897 0 2 0.693147180559945 1.570796326794897 1 -1 0.346573590279973 -0.7853981633974479 1 0 0 0 2 -2 1.039720770839918 -0.7853981633974479 2 1 0.80471895621705 0.463647609000806 catalan_values_test(): catalan_values() returns values of the Catalan numbers. N C(N) 0 1 1 1 2 2 3 5 4 14 5 42 6 132 7 429 8 1430 9 4862 10 16796 cauchy_cdf_values_test(): cauchy_cdf_values() stores values of the Cauchy CDF. MU SIGMA X cauchy_cdf(MU,SIGMA,X) 1.000000 0.500000 1.000000 0.5 1.000000 0.500000 2.000000 0.8524163823495667 1.000000 0.500000 3.000000 0.9220208696226307 1.000000 0.500000 4.000000 0.9474315432887466 1.000000 2.000000 2.000000 0.6475836176504333 1.000000 3.000000 2.000000 0.6024163823495667 1.000000 4.000000 2.000000 0.5779791303773693 1.000000 5.000000 2.000000 0.5628329581890013 2.000000 2.000000 3.000000 0.6475836176504333 3.000000 2.000000 3.000000 0.5 4.000000 2.000000 3.000000 0.3524163823495667 5.000000 2.000000 3.000000 0.25 cbrt_values_test(): cbrt_values() stores values of the cube root function. X CBRT(X) 0.000000 0.0000000000000000 -0.000000 -0.0020082988563383 0.090000 0.4481404746557165 -0.100000 -0.4641588833612779 0.400000 0.7368062997280773 -1.000000 -1.0000000000000000 2.000000 1.2599210498948732 -3.000000 -1.4422495703074083 3.141593 1.4645918875615234 -19.000000 -2.6684016487219449 29.000000 3.0723168256858471 -71.000000 -4.1408177494228529 97.000000 4.5947008922070394 -123456789.000000 -497.9338592181744616 cheby_t_poly_values_test(): cheby_t_poly_values() stores values of the Bernoulli polynomials. N X FX 0 0.800000 1 1 0.800000 0.8 2 0.800000 0.28 3 0.800000 -0.352 4 0.800000 -0.8431999999999999 5 0.800000 -0.99712 6 0.800000 -0.752192 7 0.800000 -0.2063872 8 0.800000 0.42197248 9 0.800000 0.881543168 10 0.800000 0.9884965888 11 0.800000 0.70005137408 12 0.800000 0.131585609728 cheby_t01_poly_values_test(): cheby_t01_poly_values(): values of the shifted Chebyshev T polynomials. N X FX -1 0.850000 0 0 0.850000 1 1 0.850000 0.7 2 0.850000 -0.02 3 0.850000 -0.728 4 0.850000 -0.9992 5 0.850000 -0.67088 6 0.850000 0.059968 7 0.850000 0.7548352 8 0.850000 0.99680128 9 0.850000 0.640686592 10 0.850000 -0.0998400512 11 0.850000 -0.7804626636799999 12 0.850000 -0.992807677952 7 0.000000 -1 7 0.100000 0.2063872 7 0.200000 -0.9784704 7 0.300000 0.2580224 7 0.400000 0.9870208 7 0.500000 0 7 0.600000 -0.9870208 7 0.700000 -0.2580224 7 0.800000 0.9784704 7 0.900000 -0.2063872 7 1.000000 1 cheby_u_poly_values_test(): cheby_u_poly_values() stores values of the Chebyshev U polynomials. N X FX 0 0.800000 1 1 0.800000 1.6 2 0.800000 1.56 3 0.800000 0.896 4 0.800000 -0.1264 5 0.800000 -1.09824 6 0.800000 -1.630784 7 0.800000 -1.5110144 8 0.800000 -0.78683904 9 0.800000 0.252071936 10 0.800000 1.1901541376 11 0.800000 1.65217468416 12 0.800000 1.453325357056 cheby_u01_poly_values_test(): cheby_u01_poly_values(): values of the shifted Chebyshev U polynomials. N X FX -1 0.850000 0 0 0.850000 1 1 0.850000 1.4 2 0.850000 0.96 3 0.850000 -0.056 4 0.850000 -1.0384 5 0.850000 -1.39776 6 0.850000 -0.9184639999999999 7 0.850000 0.1119104 8 0.850000 1.07513856 9 0.850000 1.393283584 10 0.850000 0.8754584576 11 0.850000 -0.16764174336 12 0.850000 -1.110156898304 7 0.000000 -8 7 0.100000 1.5110144 7 0.200000 -1.1332608 7 0.300000 -0.1636352 7 0.400000 1.0198016 7 0.500000 0 7 0.600000 -1.0198016 7 0.700000 0.1636352 7 0.800000 1.1332608 7 0.900000 -1.5110144 7 1.000000 8 cheby_v_poly_values_test(): cheby_v_poly_values() stores values of the Chebyshev V polynomials. N X FX -1 0.800000 0 0 0.800000 1 1 0.800000 0.6 2 0.800000 -0.04 3 0.800000 -0.664 4 0.800000 -1.0224 5 0.800000 -0.97184 6 0.800000 -0.532544 7 0.800000 0.1197696 8 0.800000 0.72417536 9 0.800000 1.038910976 10 0.800000 0.9380822016 11 0.800000 0.46202054656 12 0.800000 -0.198849327104 cheby_v01_poly_values_test(): cheby_v01_poly_values(): values of the shifted Chebyshev V polynomials. N X FX -1 0.850000 0 0 0.850000 1 1 0.850000 0.4 2 0.850000 -0.44 3 0.850000 -1.016 4 0.850000 -0.9824000000000001 5 0.850000 -0.35936 6 0.850000 0.479296 7 0.850000 1.0303744 8 0.850000 0.96322816 9 0.850000 0.318145024 10 0.850000 -0.5178251264 11 0.850000 -1.04310020096 12 0.850000 -0.942515154944 7 0.000000 -15 7 0.100000 3.1417984 7 0.200000 -1.3912448 7 0.300000 -1.2177792 7 0.400000 1.1837056 7 0.500000 1 7 0.600000 -0.8558976 7 0.700000 -0.8905088 7 0.800000 0.8752768 7 0.900000 0.1197696 7 1.000000 1 cheby_w_poly_values_test(): cheby_w_poly_values() stores values of the Chebyshev W polynomials. N X FX -1 0.800000 0 0 0.800000 1 1 0.800000 2.6 2 0.800000 3.16 3 0.800000 2.456 4 0.800000 0.7696 5 0.800000 -1.22464 6 0.800000 -2.729024 7 0.800000 -3.1417984 8 0.800000 -2.29785344 9 0.800000 -0.534767104 10 0.800000 1.4422260736 11 0.800000 2.84232882176 12 0.800000 3.105500041216 cheby_w01_poly_values_test(): cheby_w01_poly_values(): values of the shifted Chebyshev W polynomials. N X FX -1 0.850000 0 0 0.850000 1 1 0.850000 2.4 2 0.850000 2.36 3 0.850000 0.904 4 0.850000 -1.0944 5 0.850000 -2.43616 6 0.850000 -2.316224 7 0.850000 -0.8065536 8 0.850000 1.18704896 9 0.850000 2.468422144 10 0.850000 2.2687420416 11 0.850000 0.70781671424 12 0.850000 -1.277798641664 7 0.000000 -1 7 0.100000 -0.1197696 7 0.200000 -0.8752768 7 0.300000 0.8905088 7 0.400000 0.8558976 7 0.500000 -1 7 0.600000 -1.1837056 7 0.700000 1.2177792 7 0.800000 1.3912448 7 0.900000 -3.1417984 7 1.000000 15 chi_values_test(): chi_values() stores values of the hyperbolic cosine integral function. X CHI(X) 0.500000 -0.0527768449564936 0.600000 0.1577508933739787 0.700000 0.3455691756953907 0.800000 0.5183999848333914 0.900000 0.6813138871854340 1.000000 0.8378669409802082 1.200000 1.1418419241705950 1.400000 1.4454940757896440 1.600000 1.7595058076609651 1.800000 2.0925772140620320 2.000000 2.4526669226469151 2.500000 3.5244254883541650 3.000000 4.9603920947656102 3.500000 6.9591919276473932 4.000000 9.8135475588231866 4.500000 13.9658116485924300 chi_square_cdf_values_test(): chi_square_cdf_values() stores values of the Chi Square CDF. A X chi_square_cdf 1 0.010000 0.07965567455405796 2 0.010000 0.004987520807317687 1 0.020000 0.1124629160182849 2 0.020000 0.009950166250831945 1 0.400000 0.4729107431344619 2 0.400000 0.1812692469220181 3 0.400000 0.05975750516063926 4 0.400000 0.01752309630642177 1 1.000000 0.6826894921370859 2 1.000000 0.3934693402873666 3 1.000000 0.1987480430987992 4 1.000000 0.09020401043104986 5 1.000000 0.03743422675270363 3 2.000000 0.4275932955291202 3 3.000000 0.6083748237289111 3 4.000000 0.7385358700508894 3 5.000000 0.8282028557032669 3 6.000000 0.8883897749052874 10 1.000000 0.0001721156299558408 10 2.000000 0.003659846827343712 10 3.000000 0.01857593622214067 chi_square_pdf_values_test(): chi_square_pdf_values() stores values of the Chi Square PDF. DF X chi_square_pdf 1 0.01 3.969525474770117 2 0.01 0.4975062395963412 1 0.02 2.792879016972342 2 0.02 0.4950249168745841 1 0.4 0.5164415474672784 2 0.4 0.4093653765389909 3 0.4 0.2065766189869113 4 0.4 0.08187307530779819 1 1 0.2419707245191434 2 1 0.3032653298563167 3 1 0.2419707245191434 4 1 0.1516326649281584 5 1 0.08065690817304777 3 2 0.2075537487102974 3 3 0.1541803298037693 3 4 0.1079819330263761 3 5 0.07322491280963248 3 6 0.04865217332964145 10 1 0.0007897534631674914 10 2 0.00766415502440505 10 3 0.02353325907815472 chi_square_noncentral_cdf_values_test(): chi_square_noncentral_cdf_values(): values of the noncentral Chi Square CDF. DF LAM X chi_square_noncentral_cdf 1 0.500000 3.000000 0.8399444269398261 2 0.500000 3.000000 0.6959060300435139 3 0.500000 3.000000 0.5350879697078847 1 1.000000 3.000000 0.7647841496310313 2 1.000000 3.000000 0.6206436532195436 3 1.000000 3.000000 0.469166737537318 1 5.000000 3.000000 0.3070884345937569 2 5.000000 3.000000 0.2203818092990903 3 5.000000 3.000000 0.1500251895581519 1 20.000000 3.000000 0.003071163194335791 2 20.000000 3.000000 0.001763982670131894 3 20.000000 3.000000 0.0009816792594625021 60 30.000000 60.000000 0.01651753140866208 80 30.000000 60.000000 0.0002023419573950451 100 30.000000 60.000000 4.984476352854074e-07 1 5.000000 0.050000 0.01513252400654827 2 5.000000 0.050000 0.002090414910614367 3 5.000000 0.050000 0.0002465021206048452 10 2.000000 4.000000 0.02636835050342939 10 3.000000 4.000000 0.01857983220079215 10 4.000000 4.000000 0.0130573659548664 10 2.000000 5.000000 0.05838039534819351 10 3.000000 5.000000 0.04249784402463712 10 4.000000 5.000000 0.03082137716021596 10 2.000000 6.000000 0.1057878223400849 10 3.000000 6.000000 0.07940842984598509 10 4.000000 6.000000 0.05932010895599639 8 0.500000 5.000000 0.2110395656918684 ci_values_test(): ci_values() stores values of the cosine integral function. X CI(X) 0.500000 -0.1777840788066129 0.600000 -0.0222707069592798 0.700000 0.1005147070088978 0.800000 0.1982786159524672 0.900000 0.2760678304677729 1.000000 0.3374039229009681 1.200000 0.4204591828942405 1.400000 0.4620065850946773 1.600000 0.4717325169318778 1.800000 0.4568111294183369 2.000000 0.4229808287748650 2.500000 0.2858711963653835 3.000000 0.1196297860080003 3.500000 -0.0321285485124811 4.000000 -0.1409816978869304 4.500000 -0.1934911221017388 cin_values_test(): cin_values() stores values of the alternate cosine integral function. X CIN(X) 0.500000 0.0618525631482005 0.600000 0.0886607480948219 0.700000 0.1200260139539026 0.800000 0.1557934976348559 0.900000 0.1957873187759337 1.000000 0.2398117420005647 1.200000 0.3390780388012470 1.400000 0.4516813164280685 1.600000 0.5754867772153907 1.800000 0.7081912003853150 2.000000 0.8473820166866132 2.500000 1.2076352004103039 3.000000 1.5561981675616421 3.500000 1.8621071819093820 4.000000 2.1044917239083540 4.500000 2.2747841837795462 cinh_values_test(): cinh_values(): values of the alternate hyperbolic cosine integral function. X CINH(X) 0.000000 0.0000000000000000 0.500000 0.0631546707019188 0.600000 0.0913608522384365 0.700000 0.1250284547325902 0.800000 0.1643278712460683 0.900000 0.2094587379417273 1.000000 0.2606512760786754 1.200000 0.3823047024751071 1.400000 0.5318061742668980 1.600000 0.7122865135136963 1.800000 0.9275748842583805 2.000000 1.1823040771854361 2.500000 2.0309190915784781 3.000000 3.2845641411959670 3.500000 5.1292132942504933 4.000000 7.8500375328017622 4.500000 11.8845185869146306 clausen_values_test(): clausen_values() stores values of the Clausen integral function. X F(X) 0.001953 0.0141373528867606 0.031250 0.1395546708198128 -0.125000 -0.3849573215657424 0.500000 0.8483118777036792 1.000000 1.0139591323607684 -1.500000 -0.9392185927540921 2.000000 0.7271460508632792 2.500000 0.4335982032355328 -3.000000 -0.0980262093913014 4.000000 -0.5681439444298698 4.250000 -0.7096970178444892 -5.000000 0.9928201325469567 5.500000 -0.9812774747744737 6.000000 -0.6407826657017233 8.000000 0.8602796373323119 -10.000000 0.3907164760868021 15.000000 0.4757479392653919 20.000000 1.0105014481412877 -30.000000 0.9633208904436308 50.000000 -0.6178269948192932 clebsch_gordan_values_test(): clebsch_gordan_values() returns value of the Clebsch-Gordan coefficient. J1 J2 J3 M1 M2 M3 CG 0.50 0.50 1.00 0.50 -0.50 0.00 0.7071067811865475 0.50 0.50 1.00 0.50 0.50 1.00 1.0000000000000000 0.50 1.00 1.50 -0.50 1.00 0.50 0.5773502691896258 1.00 1.50 1.50 0.00 0.50 0.50 -0.2581988897471611 1.00 1.50 1.50 -1.00 1.50 0.50 -0.6324555320336759 1.00 1.50 1.50 0.00 1.50 1.50 -0.7745966692414834 1.00 1.00 2.00 1.00 -1.00 0.00 0.4082482904638630 1.00 1.00 2.00 0.00 0.00 0.00 0.8164965809277260 2.00 2.00 2.00 2.00 -2.00 0.00 0.5345224838248488 2.00 2.00 2.00 1.00 -1.00 0.00 0.2672612419124244 1.50 2.00 2.50 0.50 1.00 1.50 0.8944271909999159 1.50 2.00 3.50 1.50 -1.00 0.50 0.3380617018914066 collatz_count_values_test(): collatz_count_values() returns values of the length of the Collatz sequence that starts at N. N Count 1 1 2 2 3 8 4 3 5 6 6 9 7 17 8 4 9 20 10 7 27 112 50 25 100 26 200 27 300 17 400 28 500 111 600 18 700 83 800 29 cos_values_test(): cos_values() stores values of the cosine function. X COS(X) 0.000000 1.0000000000000000 0.261799 0.9659258262890683 0.500000 0.8775825618903728 0.523599 0.8660254037844386 0.785398 0.7071067811865476 1.000000 0.5403023058681398 1.047198 0.5000000000000000 1.570796 0.0000000000000000 2.000000 -0.4161468365471424 3.000000 -0.9899924966004454 3.141593 -1.0000000000000000 4.000000 -0.6536436208636119 5.000000 0.2836621854632262 cos_degree_values_test(): cos_degree_values() stores values of the cosine function. X COS(X) -5.000000 0.9961946980917455 0.000000 1.0000000000000000 1.000000 0.9998476951563913 2.000000 0.9993908270190958 3.000000 0.9986295347545738 4.000000 0.9975640502598242 5.000000 0.9961946980917455 10.000000 0.9848077530122080 15.000000 0.9659258262890683 30.000000 0.8660254037844386 45.000000 0.7071067811865476 60.000000 0.5000000000000000 75.000000 0.2588190451025207 85.000000 0.0871557427476582 86.000000 0.0697564737441253 87.000000 0.0523359562429438 88.000000 0.0348994967025010 89.000000 0.0174524064372835 90.000000 0.0000000000000000 91.000000 -0.0174524064372835 105.000000 -0.2588190451025207 180.000000 -1.0000000000000000 cos_power_int_values_test(): cos_power_int_values() stores values of the cosine power integral. A B N F 0.000000 3.141593 0 3.141592653589793 0.000000 3.141593 1 0 0.000000 3.141593 2 1.570796326794897 0.000000 3.141593 3 0 0.000000 3.141593 4 1.178097245096172 0.000000 3.141593 5 0 0.000000 3.141593 6 0.9817477042468103 0.000000 3.141593 7 0 0.000000 3.141593 8 0.8590292412159591 0.000000 3.141593 9 0 0.000000 3.141593 10 0.7731263170943632 cosh_values_test(): cosh_values() stores values of the hyperbolic cosine function. X COSH(X) -5.000000 74.2099485247878476 -1.000000 1.5430806348152437 0.000000 1.0000000000000000 0.100000 1.0050041680558035 0.200000 1.0200667556190759 0.300000 1.0453385141288605 0.400000 1.0810723718384547 0.500000 1.1276259652063807 0.600000 1.1854652182422678 0.700000 1.2551690056309430 0.800000 1.3374349463048445 0.900000 1.4330863854487743 1.000000 1.5430806348152437 2.000000 3.7621956910836314 3.000000 10.0676619957777653 4.000000 27.3082328360164865 5.000000 74.2099485247878476 10.000000 11013.2329201033226127 cot_values_test(): cot_values() stores values of the cotangent function. X COT(X) 0.083333 11.9722093536286618 0.261799 3.7320508075688772 0.500000 1.8304877217124520 0.523599 1.7320508075688772 0.785398 1.0000000000000000 1.000000 0.6420926159343308 1.047198 0.5773502691896257 1.308997 0.2679491924311227 1.570796 0.0000000000000000 1.439897 0.1316524975873959 1.505346 0.0655434628152382 2.000000 -0.4576575543602858 3.000000 -7.0152525514345339 4.000000 0.8636911544506166 5.000000 -0.2958129155327455 cp_values_test(): cp_values() stores values of the specific heat CP as a function of temperature and pressure. T P CP(T,P) 0.000000 1.000000 4.2279999999999998 100.000000 1.000000 2.0419999999999998 200.000000 1.000000 1.9750000000000001 300.000000 1.000000 2.0129999999999999 350.000000 1.000000 2.0400000000000000 400.000000 1.000000 2.0699999999999998 500.000000 1.000000 2.1349999999999998 600.000000 1.000000 2.2029999999999998 850.000000 1.000000 2.3780000000000001 1100.000000 1.000000 2.5409999999999999 1600.000000 1.000000 2.7919999999999998 2000.000000 1.000000 2.9310000000000000 0.000000 5.000000 4.2260000000000000 0.000000 10.000000 4.2229999999999999 0.000000 50.000000 4.2020000000000000 0.000000 100.000000 4.1769999999999996 0.000000 200.000000 4.1299999999999999 0.000000 300.000000 4.0890000000000004 0.000000 400.000000 4.0529999999999999 0.000000 500.000000 4.0209999999999999 0.000000 1000.000000 3.9089999999999998 0.000000 1500.000000 3.8439999999999999 0.000000 2000.000000 3.7860000000000000 0.000000 5000.000000 2.8900000000000001 datenum_values_test(): datenum_values() stores values of the MATLAB datenum for a given Y/M/D date Y M D DateNum 0 1 1 1 1 1 1 367 100 1 1 36526 1000 1 1 365244 1939 8 17 708434 1944 9 9 710284 1952 3 10 713023 1966 5 12 718199 1980 1 6 723186 1996 2 25 729080 2000 1 1 730486 dawson_values_test(): dawson_values() stores values of the Dawson integral function. X F(X) 0.000000 0.0000000000000000 0.100000 0.0993359923978529 0.200000 0.1947510333680280 0.300000 0.2826316650213119 0.400000 0.3599434819348881 0.500000 0.4244363835020223 0.600000 0.4747632036629779 0.700000 0.5105040575592318 0.800000 0.5321017070563654 0.900000 0.5407243187262987 1.000000 0.5380795069127684 1.100000 0.5262066799705525 1.200000 0.5072734964077396 1.300000 0.4833975173848241 1.400000 0.4565072375268973 1.500000 0.4282490710853986 1.600000 0.3999398943230814 1.700000 0.3725593489740788 1.800000 0.3467727691148722 1.900000 0.3229743193228178 2.000000 0.3013403889237920 debye1_values_test(): debye1_values() stores values of the Debye function of order 1. X F(X) 0.001953 0.9995118247138088 0.031250 0.9922146264712060 0.125000 0.9691839599789531 0.500000 0.8819271567906055 1.000000 0.7775046341122482 1.500000 0.6861453107894020 2.000000 0.6069472846098101 2.500000 0.5387895690778559 3.000000 0.4804352195730429 4.000000 0.3881480212979379 4.250000 0.3693080282924253 5.000000 0.3208761977001461 5.500000 0.2942399662315425 6.000000 0.2712604667850219 8.000000 0.2052393031022150 10.000000 0.1644434656799460 15.000000 0.1096619448273582 20.000000 0.0822467011782000 30.000000 0.0548311355615109 50.000000 0.0328986813369645 debye2_values_test(): debye2_values() stores values of the Debye function of order 2. X F(X) 0.001953 0.9993491172790460 0.031250 0.9896240229959918 0.125000 0.9589842620034599 0.500000 0.8437211933472536 1.000000 0.7078784756278292 1.500000 0.5914963722567128 2.000000 0.4930826439905319 2.500000 0.4107941357974967 3.000000 0.3426139606078635 4.000000 0.2405536875212790 4.250000 0.2208277006120231 5.000000 0.1723291593901414 5.500000 0.1472434673873018 6.000000 0.1266691904671579 8.000000 0.0742688059548628 10.000000 0.0479714980201219 15.000000 0.0213692016836584 20.000000 0.0120205644764464 30.000000 0.0053424751249537 50.000000 0.0019232910450554 debye3_values_test(): debye3_values() stores values of the Debye function of order 3. X F(X) 0.001953 0.9992677688598546 0.031250 0.9883300775573470 0.125000 0.9539061047202351 0.500000 0.8249629689762337 1.000000 0.6744155640778147 1.500000 0.5471066514128629 2.000000 0.4411284737276242 2.500000 0.3541360348104239 3.000000 0.2835798281434225 4.000000 0.1817369138217748 4.250000 0.1627792438511244 5.000000 0.1175974117999340 5.500000 0.0952408027231589 6.000000 0.0775813247337630 8.000000 0.0365602956731948 10.000000 0.0192957656903455 15.000000 0.0057712632276189 20.000000 0.0024352200674805 30.000000 0.0007215488221634 50.000000 0.0001558545456544 debye4_values_test(): debye4_values() stores values of the Debye function of order 4. X F(X) 0.001953 0.9992189619276157 0.031250 0.9875542528099607 0.125000 0.9508678860638974 0.500000 0.8138456917203404 1.000000 0.6548740688867369 1.500000 0.5216283096487871 2.000000 0.4118927367178853 2.500000 0.3229543485870731 3.000000 0.2518786364288331 4.000000 0.1518546125867202 4.250000 0.1337266114592141 5.000000 0.0914713776644812 5.500000 0.0712278281974625 6.000000 0.0556765478227389 8.000000 0.0219675665255750 10.000000 0.0096736755602712 15.000000 0.0019646978158352 20.000000 0.0006221464862397 30.000000 0.0001228951409208 50.000000 0.0000159272103190 dedekind_sum_values_test(): dedekind_sum_values() returns values of the Dedekind sum (N/D) = dedekind_sum ( P, Q ). P Q N D 1 1 0 1 1 2 0 1 1 3 1 18 1 4 1 8 1 5 1 5 1 6 5 18 1 7 5 14 1 8 7 16 1 9 14 27 1 10 3 5 1 11 15 22 1 12 55 72 1 13 11 13 1 14 13 14 1 15 91 90 1 16 35 32 1 17 20 17 1 18 34 27 1 19 51 38 1 20 57 40 2 1 0 1 2 3 -1 18 2 5 0 1 2 7 1 14 2 9 4 27 2 11 5 22 2 13 4 13 2 15 7 18 2 17 8 17 2 19 21 38 3 1 0 1 3 2 0 1 3 4 -1 8 3 5 0 1 3 7 -1 14 3 8 1 16 3 10 0 1 3 11 3 22 3 13 1 13 3 14 3 14 3 16 5 32 3 17 5 17 3 19 9 38 3 20 3 8 4 1 0 1 4 3 1 18 4 5 -1 5 4 7 1 14 4 9 -4 27 4 11 3 22 4 13 -1 13 4 15 19 90 4 17 0 1 4 19 11 38 5 1 0 1 5 2 0 1 5 3 -1 18 5 4 1 8 5 6 -5 18 5 7 -1 14 5 8 -1 16 5 9 4 27 5 11 -5 22 5 12 -1 72 5 13 0 1 5 14 3 14 5 16 -5 32 5 17 1 17 5 18 2 27 5 19 11 38 6 1 0 1 6 5 1 5 6 7 -5 14 6 11 5 22 6 13 -4 13 6 17 5 17 6 19 -9 38 7 1 0 1 7 2 0 1 7 3 1 18 7 4 -1 8 7 5 0 1 7 6 5 18 7 8 -7 16 7 9 -4 27 7 10 0 1 7 11 -3 22 7 12 1 72 7 13 4 13 7 15 -7 18 7 16 -3 32 7 17 1 17 7 18 -2 27 7 19 3 38 7 20 3 8 dielectric_values_test(): dielectric_values() stores values of the dielectric function. T P EPS(T,P) 0.000000 100.000000 88.2900000000000063 0.000000 500.000000 90.0699999999999932 0.000000 1000.000000 92.0199999999999960 0.000000 2000.000000 95.1400000000000006 0.000000 5000.000000 100.7699999999999960 25.000000 100.000000 78.8499999999999943 50.000000 100.000000 70.2699999999999960 75.000000 100.000000 62.6000000000000014 100.000000 100.000000 55.7800000000000011 150.000000 100.000000 44.3100000000000023 200.000000 100.000000 35.1099999999999994 300.000000 100.000000 20.3999999999999986 400.000000 100.000000 1.1699999999999999 500.000000 100.000000 1.1100000000000001 600.000000 100.000000 1.0800000000000001 dilogarithm_values_test(): dilogarithm_values() stores values of the dilogarithm function. X F(X) 0.000000 0.0000000000000000 0.050000 0.0506392924644960 0.100000 0.1026177910993911 0.150000 0.1560350339454831 0.200000 0.2110037754397048 0.250000 0.2676526390827326 0.300000 0.3261295100754761 0.350000 0.3866059411605865 0.400000 0.4492829744712817 0.450000 0.5143989891542119 0.500000 0.5822405264650125 0.550000 0.6531576315069018 0.600000 0.7275863077163334 0.650000 0.8060826895177240 0.700000 0.8893776242860387 0.750000 0.9784693929303061 0.800000 1.0747946000082480 0.850000 1.1805811238302550 0.900000 1.2997147230049590 0.950000 1.4406337969700389 1.000000 1.6449340668482260 dixon_elliptic_values_test(): dixon_elliptic_values() stores values of the Dixon elliptic functions CM(X), SM(X). X C S C^3+S^3 0.000000 1.000000 0.000000 1.000000 0.100000 0.999667 0.099983 1.000001 0.200000 0.997337 0.199734 1.000000 0.300000 0.991040 0.298657 0.999999 0.400000 0.978892 0.395785 1.000001 0.500000 0.959182 0.489826 1.000000 0.600000 0.930494 0.579255 1.000001 0.700000 0.891817 0.662445 0.999999 0.800000 0.842651 0.737828 1.000000 0.900000 0.783054 0.804069 1.000000 1.000000 0.713636 0.860228 1.000000 1.100000 0.635486 0.905873 1.000001 1.200000 0.550033 0.941134 0.999999 1.300000 0.458886 0.966693 1.000001 1.400000 0.363655 0.983705 0.999999 1.500000 0.265799 0.993701 1.000000 1.600000 0.166510 0.998459 1.000001 1.700000 0.066636 0.999901 0.999999 1.800000 -0.033362 1.000010 0.999993 1.900000 -0.133414 1.000790 0.999997 2.000000 -0.233857 1.004250 1.000015 e1_values_test(): e1_values() stores values of the exponential integral. X E1(X) 0.500000 0.5597735947761608 0.600000 0.4543795031894021 0.700000 0.3737688432335091 0.800000 0.3105965785455430 0.900000 0.2601839393259996 1.000000 0.2193839343955203 1.100000 0.1859909045360402 1.200000 0.1584084368514626 1.300000 0.1354509578491291 1.400000 0.1162193125713579 1.500000 0.1000195824066327 1.600000 0.0863083336975398 1.700000 0.0746546444012531 1.800000 0.0647131293638689 1.900000 0.0562043781745349 2.000000 0.0489005107080611 easter_gregorian_values_test(): easter_gregorian_values() stores values of the date of Easter in the Gregorian calendar. D M Y 30 3 1997 12 4 1998 4 4 1999 23 4 2000 15 4 2001 31 3 2002 20 4 2003 11 4 2004 27 3 2005 16 4 2006 easter_julian_values_test(): easter_julian_values() stores values of the date of Easter in the Julian calendar. D M Y 30 3 1997 12 4 1998 4 4 1999 23 4 2000 15 4 2001 31 3 2002 20 4 2003 11 4 2004 27 3 2005 16 4 2006 ei_values_test(): ei_values() stores values of the exponential integral. X EI(X) 0.500000 0.4542199048631736 0.600000 0.7698812899373594 0.700000 1.0649071946242910 0.800000 1.3473965482123260 0.900000 1.6228117136968669 1.000000 1.8951178163559370 1.100000 2.1673782795634029 1.200000 2.4420922851926519 1.300000 2.7213988802320239 1.400000 3.0072074641506461 1.500000 3.3012854491297978 1.600000 3.6053199490194690 1.700000 3.9209632013549038 1.800000 4.2498675574879341 1.900000 4.5937136869535848 2.000000 4.9542343560018898 elliptic_ea_values_test(): elliptic_ea_values() stores values of the complete elliptic integral of the second kind, with parameter A in degrees. A E(A) 0.000000 1.5707963267948970 5.000000 1.5678090739776220 10.000000 1.5588871966015960 15.000000 1.5441504969146731 20.000000 1.5237992052597740 25.000000 1.4981149284221160 30.000000 1.4674622093394269 35.000000 1.4322909693067560 40.000000 1.3931402485238120 45.000000 1.3506438810476760 50.000000 1.3055390942977940 55.000000 1.2586796247799970 60.000000 1.2110560275684590 65.000000 1.1638279644931391 70.000000 1.1183777379698641 75.000000 1.0764051130764030 80.000000 1.0401143957060099 85.000000 1.0126635062343960 90.000000 1.0000000000000000 elliptic_ek_values_test(): elliptic_ek_values() stores values of the complete elliptic integral of the second kind, with parameter K. K E(K) 0.000000 1.5707963267948970 0.223607 1.5509733517804720 0.316228 1.5307576368977629 0.387298 1.5101218320928189 0.447214 1.4890350580958529 0.500000 1.4674622093394269 0.547723 1.4453630644126649 0.591608 1.4226911334908789 0.632456 1.3993921388974320 0.670820 1.3754019718711159 0.707107 1.3506438810476760 0.741620 1.3250244979582300 0.774597 1.2984280350469131 0.806226 1.2707074796501490 0.836660 1.2416705679458231 0.866025 1.2110560275684590 0.894427 1.1784899243278391 0.921954 1.1433957918831661 0.948683 1.1047747327040729 0.974679 1.0604737277662779 1.000000 1.0000000000000000 elliptic_em_values_test(): elliptic_em_values() stores values of the complete elliptic integral of the second kind, with parameter modulus M. M E(M) 0.000000 1.5707963267948970 0.050000 1.5509733517804720 0.100000 1.5307576368977629 0.150000 1.5101218320928189 0.200000 1.4890350580958529 0.250000 1.4674622093394269 0.300000 1.4453630644126649 0.350000 1.4226911334908789 0.400000 1.3993921388974320 0.450000 1.3754019718711159 0.500000 1.3506438810476760 0.550000 1.3250244979582300 0.600000 1.2984280350469131 0.650000 1.2707074796501490 0.700000 1.2416705679458231 0.750000 1.2110560275684590 0.800000 1.1784899243278391 0.850000 1.1433957918831661 0.900000 1.1047747327040729 0.950000 1.0604737277662779 1.000000 1.0000000000000000 elliptic_fa_values_test(): elliptic_fa_values() stores values of the complete elliptic integral of the first kind, with parameter A in degrees. A F(A) 0.000000 1.5707963267948970 5.000000 1.5737921309247680 10.000000 1.5828428043383509 15.000000 1.5981420021125401 20.000000 1.6200258991242040 25.000000 1.6489952184785299 30.000000 1.6857503548125961 35.000000 1.7312451756570579 40.000000 1.7867691348850210 45.000000 1.8540746773013721 50.000000 1.9355810960047219 55.000000 2.0347153121857908 60.000000 2.1565156474996430 65.000000 2.3087867981671959 70.000000 2.5045500790016342 75.000000 2.7680631453687679 80.000000 3.1533852518878391 85.000000 3.8317419997841462 elliptic_fk_values_test(): elliptic_fk_values() stores values of the complete elliptic integral of the first kind, with parameter KM. K F(K) 0.000000 1.5707963267948970 0.223607 1.5910034537907920 0.316228 1.6124413487202189 0.387298 1.6352567322645799 0.447214 1.6596235986105281 0.500000 1.6857503548125961 0.547723 1.7138894481787910 0.591608 1.7443505972256130 0.632456 1.7775193714912529 0.670820 1.8138839368169830 0.707107 1.8540746773013721 0.741620 1.8989249102715540 0.774597 1.9495677498060260 0.806226 2.0075983984243759 0.836660 2.0753631352924691 0.866025 2.1565156474996430 0.894427 2.2572053268208538 0.921954 2.3890164863255801 0.948683 2.5780921133481729 0.974679 2.9083372484445520 elliptic_fm_values_test(): elliptic_fm_values() stores values of the complete elliptic integral of the first kind, with parameter modulus M. M F(M) 0.000000 1.5707963267948970 0.050000 1.5910034537907920 0.100000 1.6124413487202189 0.150000 1.6352567322645799 0.200000 1.6596235986105281 0.250000 1.6857503548125961 0.300000 1.7138894481787910 0.350000 1.7443505972256130 0.400000 1.7775193714912529 0.450000 1.8138839368169830 0.500000 1.8540746773013721 0.550000 1.8989249102715540 0.600000 1.9495677498060260 0.650000 2.0075983984243759 0.700000 2.0753631352924691 0.750000 2.1565156474996430 0.800000 2.2572053268208538 0.850000 2.3890164863255801 0.900000 2.5780921133481729 0.950000 2.9083372484445520 elliptic_pia_values_test(): elliptic_pia_values() stores values of the complete elliptic integral of the third kind, with parameter A in degrees. N A Pi(N,A) -10.000000 30.000000 0.4892245275965397 -10.000000 45.000000 0.5106765677902629 -10.000000 60.000000 0.5460409271920561 -10.000000 77.079034 0.6237325893535237 -3.000000 30.000000 0.8230455426606750 -3.000000 45.000000 0.8760028274011437 -3.000000 60.000000 0.9660073560143946 -3.000000 77.079034 1.1719523914817980 -1.000000 30.000000 1.1774468430005660 -1.000000 45.000000 1.2731273667496821 -1.000000 60.000000 1.4400343186575510 -1.000000 77.079034 1.8364721723025910 0.000000 30.000000 1.6857503548125961 0.000000 45.000000 1.8540746773013721 0.000000 60.000000 2.1565156474996430 0.000000 77.079034 2.9083372484445520 0.500000 30.000000 2.4136715042011949 0.500000 45.000000 2.7012877620953510 0.500000 60.000000 3.2347734712494649 0.500000 77.079034 4.6333081472798909 elliptic_pik_values_test(): elliptic_pik_values() stores values of the complete elliptic integral of the third kind, with parameter K. N K Pi(N,K) -10.000000 0.500000 0.4892245275965397 -10.000000 0.707107 0.5106765677902629 -10.000000 0.866025 0.5460409271920561 -10.000000 0.974679 0.6237325893535237 -3.000000 0.500000 0.8230455426606750 -3.000000 0.707107 0.8760028274011437 -3.000000 0.866025 0.9660073560143946 -3.000000 0.974679 1.1719523914817980 -1.000000 0.500000 1.1774468430005660 -1.000000 0.707107 1.2731273667496821 -1.000000 0.866025 1.4400343186575510 -1.000000 0.974679 1.8364721723025910 0.000000 0.500000 1.6857503548125961 0.000000 0.707107 1.8540746773013721 0.000000 0.866025 2.1565156474996430 0.000000 0.974679 2.9083372484445520 0.500000 0.500000 2.4136715042011949 0.500000 0.707107 2.7012877620953510 0.500000 0.866025 3.2347734712494649 0.500000 0.974679 4.6333081472798909 elliptic_pim_values_test(): elliptic_pim_values() stores values of the complete elliptic integral of the third kind, with parameter M. N M Pi(N,M) -10.000000 0.250000 0.4892245275965397 -10.000000 0.500000 0.5106765677902629 -10.000000 0.750000 0.5460409271920561 -10.000000 0.950000 0.6237325893535237 -3.000000 0.250000 0.8230455426606750 -3.000000 0.500000 0.8760028274011437 -3.000000 0.750000 0.9660073560143946 -3.000000 0.950000 1.1719523914817980 -1.000000 0.250000 1.1774468430005660 -1.000000 0.500000 1.2731273667496821 -1.000000 0.750000 1.4400343186575510 -1.000000 0.950000 1.8364721723025910 0.000000 0.250000 1.6857503548125961 0.000000 0.500000 1.8540746773013721 0.000000 0.750000 2.1565156474996430 0.000000 0.950000 2.9083372484445520 0.500000 0.250000 2.4136715042011949 0.500000 0.500000 2.7012877620953510 0.500000 0.750000 3.2347734712494649 0.500000 0.950000 4.6333081472798909 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 erf_values_test(): erf_values() stores values of the error function. X ERF(X) 0.000000 0.0000000000000000 0.100000 0.1124629160182849 0.200000 0.2227025892104785 0.300000 0.3286267594591274 0.400000 0.4283923550466685 0.500000 0.5204998778130465 0.600000 0.6038560908479259 0.700000 0.6778011938374185 0.800000 0.7421009647076605 0.900000 0.7969082124228321 1.000000 0.8427007929497149 1.100000 0.8802050695740817 1.200000 0.9103139782296354 1.300000 0.9340079449406524 1.400000 0.9522851197626488 1.500000 0.9661051464753106 1.600000 0.9763483833446440 1.700000 0.9837904585907746 1.800000 0.9890905016357306 1.900000 0.9927904292352575 2.000000 0.9953222650189527 erfc_values_test(): erfc_values() stores values of the complementary error function. X ERFC(X) 0.000000 1.0000000000000000 0.200000 0.7772974107895215 0.400000 0.5716076449533315 0.600000 0.3961439091520741 0.800000 0.2578990352923395 1.000000 0.1572992070502851 1.200000 0.0896860217703646 1.400000 0.0477148802373512 1.600000 0.0236516166553560 1.800000 0.0109094983642693 2.000000 0.0046777349810473 2.200000 0.0018628462979819 2.400000 0.0006885138966451 2.600000 0.0002360344165293 2.800000 0.0000750131946655 3.000000 0.0000220904969986 3.200000 0.0000060257611518 3.400000 0.0000015219933629 3.600000 0.0000003558629930 3.800000 0.0000000770039275 4.000000 0.0000000154172579 euler_number_values_test(): euler_number_values() returns values of the Euler numbers. N euler_number(N) 0 1 1 0 2 -1 4 5 6 -61 8 1385 10 -50521 12 2702765 euler_poly_values_test(): euler_poly_values() stores values of the Euler polynomials. N X FX 0 0.200000 1 1 0.200000 -0.3 2 0.200000 -0.16 3 0.200000 0.198 4 0.200000 0.1856 5 0.200000 -0.40368 6 0.200000 -0.560896 7 0.200000 1.7187888 8 0.200000 3.18043136 9 0.200000 -12.539467008 10 0.200000 -28.9999384576 5 -0.500000 -0.0625 5 -0.400000 -0.17424 5 -0.300000 -0.29768 5 -0.200000 -0.40432 5 -0.100000 -0.47526 5 0.000000 -0.5 5 0.100000 -0.47524 5 0.200000 -0.40368 5 0.300000 -0.29282 5 0.400000 -0.15376 5 0.500000 0 5 0.600000 0.15376 5 0.700000 0.29282 5 0.800000 0.40368 5 0.900000 0.47524 5 1.000000 0.5 exp_values_test(): exp_values() stores values of the exponential function. X F(X) -10.000000 0.0000453999297625 -5.000000 0.0067379469990855 -1.000000 0.3678794411714423 0.000000 1.0000000000000000 0.000000 1.0000000099999999 0.000100 1.0001000050001667 0.001000 1.0010005001667084 0.010000 1.0100501670841679 0.100000 1.1051709180756477 0.200000 1.2214027581601699 0.300000 1.3498588075760032 0.400000 1.4918246976412703 0.500000 1.6487212707001282 0.600000 1.8221188003905089 0.700000 2.0137527074704766 0.800000 2.2255409284924674 0.900000 2.4596031111569499 1.000000 2.7182818284590451 2.000000 7.3890560989306504 3.141593 23.1406926327792704 5.000000 148.4131591025765999 10.000000 22026.4657948067178950 20.000000 485165195.4097902774810791 40.000000 235385266837020000.0000000000000000 exp3_int_values_test(): exp3_int_values() stores values of the exp3 integral. X F(X) 0.001953 0.0019531249963620 0.007812 0.0078124990686776 0.031250 0.0312497615834997 0.125000 0.1249389988880308 0.500000 0.4849171431136397 1.000000 0.8075111821396714 1.250000 0.8688926541262327 1.500000 0.8886172223535717 1.875000 0.8928601850021818 2.000000 0.8929535142938763 2.125000 0.8929747911273784 2.250000 0.8929788057979812 2.500000 0.8929795031749662 2.750000 0.8929795115295190 3.000000 0.8929795115691812 3.125000 0.8929795115692474 3.250000 0.8929795115692492 3.500000 0.8929795115692493 3.750000 0.8929795115692493 4.000000 0.8929795115692493 exponential_01_pdf_values_test(): exponential_01_pdf_values() stores values of the unit exponential PDF. X exponential_01_pdf(X) 0.701301 0.4959398481993681 4.75975 0.00856777959135697 4.0623 0.01720937842266235 2.58932 0.07507070056996956 1.78419 0.1679332083261492 -0.136347 0 0.916678 0.399845179478639 0.104762 0.9005384971416223 -0.258941 0 2.98681 0.05044803826563792 exponential_cdf_values_test(): exponential_cdf_values() stores values of the exponential CDF. LAM X F 0.500000 1.000000 0.3934693402873666 0.500000 2.000000 0.6321205588285577 0.500000 3.000000 0.7768698398515702 0.500000 4.000000 0.8646647167633873 1.000000 2.000000 0.8646647167633873 2.000000 2.000000 0.9816843611112658 3.000000 2.000000 0.9975212478233336 4.000000 2.000000 0.9996645373720975 5.000000 2.000000 0.9999546000702375 exponential_pdf_values_test(): exponential_pdf_values() stores values of the exponential PDF. BETA X F 1.09209 9.55881 0.0001446999730194618 4.14755 5.57312 0.06289850821824726 2.07654 0.567799 0.3663607831924032 1.28789 1.01056 0.3542787877169571 0.219145 6.30305 1.472582451176006e-12 0.308636 4.44034 1.829637907028298e-06 2.00653 7.5222 0.01173398427218792 3.98643 -0.0814325 0 4.48752 3.4426 0.1034724689882351 0.472724 0.0375306 1.95394780436833 extreme_values_cdf_values_test(): extreme_values_cdf_values() stores values of the Extreme Values CDF. Alpha Beta X CDF 1.000000 0.500000 1.000000 0.3678794411714423 1.000000 0.500000 2.000000 0.8734230184931167 1.000000 0.500000 3.000000 0.9818510730616665 1.000000 0.500000 4.000000 0.9975243173927525 1.000000 2.000000 2.000000 0.545239211892605 1.000000 3.000000 2.000000 0.4884435800065159 1.000000 4.000000 2.000000 0.4589560693076638 1.000000 5.000000 2.000000 0.4409910259429826 2.000000 2.000000 3.000000 0.545239211892605 3.000000 2.000000 3.000000 0.3678794411714423 4.000000 2.000000 3.000000 0.1922956455479649 5.000000 2.000000 3.000000 0.06598803584531254 f_cdf_values_test(): f_cdf_values() stores values of the F CDF. A B X f_cdf(A,B,X) 1 1 1.000000 0.5 1 5 0.528000 0.4999714850534485 5 1 1.890000 0.499603437017099 1 5 1.690000 0.7496993658293228 2 10 1.600000 0.7504656462757382 4 20 1.470000 0.7514156325324275 1 5 4.060000 0.8999867031372156 6 6 3.050000 0.8997127554259698 8 16 2.090000 0.9002845660853669 1 5 6.610000 0.9500248817817623 3 10 3.710000 0.9500574946122442 6 12 3.000000 0.95019264 1 5 10.010000 0.9750133887312993 1 5 16.260000 0.9900022327445249 1 5 22.780000 0.9949977837872073 1 5 47.180000 0.9989999621122122 2 5 1.000000 0.5687988496283078 3 5 1.000000 0.5351452100063649 4 5 1.000000 0.5143428032407864 5 5 1.000000 0.5 f_noncentral_cdf_values_test(): f_noncentral_cdf_values() stores values of the noncentral F CDF. A B LAM X F 1 1 0.000000 1.000000 0.5 1 5 0.000000 1.000000 0.6367825323508775 1 5 0.250000 1.000000 0.5840916116305482 1 5 1.000000 0.500000 0.3234431872392788 1 5 1.000000 1.000000 0.450118787981355 1 5 1.000000 2.000000 0.6078881441188312 1 5 1.000000 3.000000 0.7059275551414605 1 5 1.000000 4.000000 0.7721782003263727 1 5 1.000000 5.000000 0.8191049017635073 1 5 2.000000 1.000000 0.3170348430749965 2 5 1.000000 1.000000 0.4327218008454471 2 10 1.000000 1.000000 0.4502696915707327 3 5 1.000000 1.000000 0.4261881186594096 3 5 2.000000 1.000000 0.6753687206341544 4 5 1.000000 1.000000 0.4229108778879005 4 5 1.000000 2.000000 0.6927667261228938 5 1 0.000000 1.000000 0.3632174676491226 5 5 1.000000 1.000000 0.4210054012695865 6 6 1.000000 1.000000 0.4266672258818927 6 12 1.000000 1.000000 0.4464016600524644 8 16 1.000000 2.000000 0.8445888579504827 16 8 1.000000 2.000000 0.4339300273343604 factorial_values_test(): factorial_values() returns values of the integer factorial function. N factorial(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() stores values of the Fresnel cosine integral. X F 0.000000 0.0000000000000000 0.200000 0.1999210575944531 0.400000 0.3974807591723594 0.600000 0.5810954469916523 0.800000 0.7228441718963561 1.000000 0.7798934003768228 1.200000 0.7154377229230734 1.400000 0.5430957835462564 1.600000 0.3654616834404877 1.800000 0.3336329272215571 2.000000 0.4882534060753408 2.200000 0.6362860449033195 2.400000 0.5549614058564281 2.600000 0.3889374961919690 2.800000 0.4674916516989059 3.000000 0.6057207892976856 fresnel_sin_values_test(): fresnel_sin_values() stores values of the Fresnel sine integral. X F 0.000000 0.0000000000000000 0.200000 0.0041876091616568 0.400000 0.0333594326606132 0.600000 0.1105402073593870 0.800000 0.2493413930539178 1.000000 0.4382591473903548 1.200000 0.6234009185462497 1.400000 0.7135250773634121 1.600000 0.6388876835093809 1.800000 0.4509387692675831 2.000000 0.3434156783636982 2.200000 0.4557046121246569 2.400000 0.6196899649456836 2.600000 0.5499893231527195 2.800000 0.3915284435431718 3.000000 0.4963129989673750 frobenius_number_data_values_test(): frobenius_number_data_values() returns the 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() stores values of the Gamma function. X GAMMA(X) -0.500000 -3.5449077018110322 -0.010000 -100.5871979644108052 0.010000 99.4325851191506018 0.100000 9.5135076986687324 0.200000 4.5908437119988026 0.400000 2.2181595437576882 0.500000 1.7724538509055161 0.600000 1.4891922488128171 0.800000 1.1642297137253030 1.000000 1.0000000000000000 1.100000 0.9513507698668732 1.200000 0.9181687423997607 1.300000 0.8974706963062772 1.400000 0.8872638175030753 1.500000 0.8862269254527581 1.600000 0.8935153492876903 1.700000 0.9086387328532904 1.800000 0.9313837709802427 1.900000 0.9617658319073874 2.000000 1.0000000000000000 3.000000 2.0000000000000000 4.000000 6.0000000000000000 10.000000 362880.0000000000000000 20.000000 121645100408832000.0000000000000000 30.000000 8841761993739701898620088352768.0000000000000000 gamma_01_pdf_values_test(): gamma_01_pdf_values() stores values of the standard Gamma PDF. ALPHA X PDF 1.09209 9.54133 9.260811963612823e-05 4.14755 5.3978 0.1260335478747823 2.07654 0.194247 0.1363536772414351 1.28789 0.654546 0.5114450139194701 0.219145 6.15664 0.0001230139468263628 0.308636 4.22016 0.001870342832511005 2.00653 7.42407 0.004476000451227789 3.98643 -0.480697 0 4.48752 3.1829 0.2056668486524041 0.472724 -0.357023 0 gamma_inc_values_test(): gamma_inc_values() stores values of the incomplete Gamma function. A X gamma_inc(A,X) 0.100000 0.030000 2.49030283630057 0.100000 0.300000 0.8718369702247978 0.100000 1.500000 0.1079213896175866 0.500000 0.075000 1.238121685818417 0.500000 0.750000 0.3911298052193973 0.500000 3.500000 0.01444722098952533 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.006737946999085467 1.100000 0.100000 0.8827966752611692 1.100000 1.000000 0.3908330082003269 1.100000 5.000000 0.008051456628620992 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.00729505572443613 6.000000 2.500000 114.9574754165633 6.000000 12.000000 2.440923530031405 11.000000 16.000000 280854.6620274718 26.000000 25.000000 8.576480283455533e+24 41.000000 45.000000 2.085031346403364e+47 gamma_inc_p_values_test(): gamma_inc_p_values() stores values of an incomplete Gamma function. A X gamma_inc_p(A,X) 0.100000 0.030000 0.7382350532339351 0.100000 0.300000 0.9083579897300343 0.100000 1.500000 0.9886559833621947 0.500000 0.075000 0.3014646416966613 0.500000 0.750000 0.7793286380801532 0.500000 3.500000 0.9918490284064972 1.000000 0.100000 0.09516258196404043 1.000000 1.000000 0.6321205588285577 1.000000 5.000000 0.9932620530009145 1.100000 0.100000 0.07205974576054322 1.100000 1.000000 0.5891809618706485 1.100000 5.000000 0.9915368159845525 2.000000 0.150000 0.01018582711118352 2.000000 1.500000 0.4421745996289254 2.000000 7.000000 0.9927049442755639 6.000000 2.500000 0.04202103819530612 6.000000 12.000000 0.9796589705830716 11.000000 16.000000 0.9226039842296428 26.000000 25.000000 0.4470785799755852 41.000000 45.000000 0.7444549220718699 gamma_inc_q_values_test(): gamma_inc_q_values() stores values of an incomplete Gamma function. A X gamma_inc_q(A,X) 0.100000 0.030000 0.2617649467660649 0.100000 0.300000 0.09164201026996573 0.100000 1.500000 0.01134401663780527 0.500000 0.075000 0.6985353583033387 0.500000 0.750000 0.2206713619198468 0.500000 3.500000 0.0081509715935027 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.006737946999085467 1.100000 0.100000 0.9279402542394568 1.100000 1.000000 0.4108190381293515 1.100000 5.000000 0.008463184015447498 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.00729505572443613 6.000000 2.500000 0.9579789618046939 6.000000 12.000000 0.02034102941692837 11.000000 16.000000 0.07739601577035708 26.000000 25.000000 0.5529214200244148 41.000000 45.000000 0.2555450779281301 gamma_log_values: gamma_log_values() stores values of the logarithm of the Gamma function. X gamma_log(X) 0.200000 1.5240638224307841 0.400000 0.7966778177017837 0.600000 0.3982338580692348 0.800000 0.1520596783998375 1.000000 0.0000000000000000 1.100000 -0.0498724412598397 1.200000 -0.0853740900033158 1.300000 -0.1081748095078604 1.400000 -0.1196129141723712 1.500000 -0.1207822376352452 1.600000 -0.1125917656967557 1.700000 -0.0958076974070659 1.800000 -0.0710838729143722 1.900000 -0.0389842759230833 2.000000 0.0000000000000000 3.000000 0.6931471805599453 4.000000 1.7917594692280550 10.000000 12.8018274800814691 20.000000 39.3398841871994946 30.000000 71.2570389671680147 gamma_pdf_values_test(): gamma_pdf_values() stores values of the standard Gamma PDF. BETA ALPHA X PDF 1.09209 4.78159 4.94296 0.1672017697220646 2.80848 2.07654 0.209936 0.8522122814089312 1.28789 0.549784 0.0717398 2.122272611165834 3.16983 0.308636 2.58714 6.993771842317114e-05 2.00653 3.77337 4.74318 0.01679379733182281 0.00919186 4.48752 1.97466 6.687464259463117e-10 0.472724 0.0680845 5.1264 0.001295436045931343 4.20424 0.61552 -0.153423 0 1.30151 4.56242 0.504717 0.01189893036865762 1.75814 4.11444 1.45622 0.3658836103539945 gaussian_prime_complex_values_test(): gaussian_prime_complex_values() stores values of complex Gaussian primes. p.real p.imag -5 -4 -5 -2 -5 2 -4 -5 -3 -2 -3 0 -2 -5 -2 -1 -1 -2 -1 -1 0 3 1 -4 1 -2 1 -1 2 -3 3 0 4 1 5 4 gaussian_prime_real_values_test(): gaussian_prime_real_values() stores values of real Gaussian primes. p 3 7 11 19 23 31 43 47 59 67 71 79 83 103 211 307 419 503 gcd_values_test(): gcd_values() returns values of the greatest common divisor. 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_polynomial_values_test(): gegenbauer_polynomial_values() stores values of the Gegenbauer polynomials. N A X FX 0 0.500000 0.200000 1 1 0.500000 0.200000 0.2 2 0.500000 0.200000 -0.44 3 0.500000 0.200000 -0.28 4 0.500000 0.200000 0.232 5 0.500000 0.200000 0.30752 6 0.500000 0.200000 -0.08057599999999999 7 0.500000 0.200000 -0.2935168 8 0.500000 0.200000 -0.0395648 9 0.500000 0.200000 0.2459712 10 0.500000 0.200000 0.1290720256 2 0.000000 0.400000 0 2 1.000000 0.400000 -0.36 2 2.000000 0.400000 -0.08 2 3.000000 0.400000 0.84 2 4.000000 0.400000 2.4 2 5.000000 0.400000 4.6 2 6.000000 0.400000 7.44 2 7.000000 0.400000 10.92 2 8.000000 0.400000 15.04 2 9.000000 0.400000 19.8 2 10.000000 0.400000 25.2 5 3.000000 -0.500000 -9 5 3.000000 -0.400000 -0.16128 5 3.000000 -0.300000 -6.67296 5 3.000000 -0.200000 -8.37504 5 3.000000 -0.100000 -5.52672 5 3.000000 0.000000 0 5 3.000000 0.100000 5.52672 5 3.000000 0.200000 8.37504 5 3.000000 0.300000 6.67296 5 3.000000 0.400000 0.16128 5 3.000000 0.500000 -9 5 3.000000 0.600000 -15.42528 5 3.000000 0.700000 -9.696960000000001 5 3.000000 0.800000 22.44096 5 3.000000 0.900000 100.88928 5 3.000000 1.000000 252 geometric_cdf_values_test(): geometric_cdf_values() stores values of the Geometric CDF. X P geometric_cdf(X,P) 1 0.1 0.19 2 0.1 0.271 3 0.1 0.3439 10 0.1 0.6861894039100001 1 0.2 0.36 2 0.2 0.488 3 0.2 0.5904 10 0.2 0.91410065408 3 0.3 0.7599 3 0.4 0.8704 3 0.5 0.9375 5 0.5 0.984375 10 0.5 0.99951171875 3 0.9 0.9999 goodwin_values: goodwin_values() stores values of the Goodwin function. X GOODWIN(X) 0.001953 5.9531540040441655 0.007812 4.5769601268624491 0.031250 3.2288921331902216 0.125000 1.9746110873568719 0.500000 0.9635604620869773 1.000000 0.6051336525033446 1.250000 0.5130550645953220 1.500000 0.4459860282094613 1.875000 0.3734445820687975 2.000000 0.3543359288495306 2.125000 0.3371215651888192 2.500000 0.2943617072936298 3.000000 0.2519349964489722 3.500000 0.2202877822212394 4.000000 0.1957525823769892 4.500000 0.1761630316667070 5.000000 0.1601546947966478 5.750000 0.1409611687619339 6.000000 0.1355498719104907 7.000000 0.1175160506008510 gud_values: gud_values() stores values of the Gudermannian function. X GUD(X) -2.000000 -1.3017603360460150 -1.000000 -0.8657694832396586 0.000000 0.0000000000000000 0.100000 0.0998337487934866 0.200000 0.1986798470079397 0.500000 0.4803810791337294 1.000000 0.8657694832396586 1.500000 1.1317283452505089 2.000000 1.3017603360460150 2.500000 1.4069935689361539 3.000000 1.4713043411171931 3.500000 1.5104199075457001 4.000000 1.5341691443347329 harmonic_values_test(): harmonic_values() stores values of the Harmonic number sequence. N H(N) 1 1.0000000000000000 2 1.5000000000000000 3 1.8333333333333330 4 2.0833333333333330 5 2.2833333333333332 6 2.4500000000000002 7 2.5928571428571430 8 2.7178571428571430 9 2.8289682539682541 10 2.9289682539682542 11 3.0198773448773450 12 3.1032106782106781 13 3.1801337551337552 14 3.2515623265623268 15 3.3182289932289928 16 3.3807289932289928 17 3.4395525226407582 18 3.4951080781963131 19 3.5477396571436821 20 3.5977396571436819 21 3.6453587047627298 22 3.6908132502172748 23 3.7342915110868402 24 3.7759581777535072 25 3.8159581777535072 26 3.8544197162150451 27 3.8914567532520818 28 3.9271710389663679 29 3.9616537975870578 30 3.9949871309203910 31 4.0272451954365200 32 4.0584951954365200 33 4.0887982257395503 34 4.1182099904454326 35 4.1467814190168610 36 4.1745591967946387 37 4.2015862238216659 38 4.2279020132953500 39 4.2535430389363764 40 4.2785430389363759 hermite_function_values_test(): hermite_function_values() stores values of the Hermite function. N X F 0 0 0.7511255444649425 1 0 0 2 0 -0.5311259660135985 3 0 0 4 0 0.4599685791773266 5 0 0 0 1 0.4555806720113325 1 1 0.6442883651134752 2 1 0.3221441825567376 3 1 -0.2630296236233334 4 1 -0.464975076292511 5 1 -0.05881521185179581 6 1 0.3905052515434106 7 1 0.2631861423064045 8 1 -0.2336911435996523 9 1 -0.358297336147284 10 1 0.06146344487883041 11 1 0.3678312067984882 12 1 0.09131969309166278 5 0.5 0.4385750950032321 5 2 -0.02624689527931006 5 3 0.5138426125477819 5 4 0.09355563118061758 hermite_poly_phys_values_test(): hermite_poly_phys_values() stores values of the Hermite physicist polynomials. N X FX 0 5.000000 1 1 5.000000 10 2 5.000000 98 3 5.000000 940 4 5.000000 8812 5 5.000000 80600 6 5.000000 717880 7 5.000000 6211600 8 5.000000 52065680 9 5.000000 421271200 10 5.000000 3275529760 11 5.000000 24329873600 12 5.000000 171237081280 5 0.000000 0 5 0.500000 41 5 1.000000 -8 5 3.000000 3816 5 10.000000 3041200 hermite_poly_prob_values_test(): hermite_poly_prob_values() stores values of the Hermite probabilist polynomials. N X FX 0 5.000000 1 1 5.000000 5 2 5.000000 24 3 5.000000 110 4 5.000000 478 5 5.000000 1950 6 5.000000 7360 7 5.000000 25100 8 5.000000 73980 9 5.000000 169100 10 5.000000 179680 11 5.000000 -792600 12 5.000000 -5939480 5 0.000000 0 5 0.500000 6.28125 5 1.000000 6 5 3.000000 18 5 10.000000 90150 hyper_1f1_values_test(): hyper_1f1_values() stores values of the hypergeometric function 1F1 A B X F -2.5 3.3 0.25 0.8187992668926519 -0.5 1.1 0.25 0.8828398482803297 0.5 1.1 0.25 1.124502376495263 2.5 3.3 0.25 1.21010493016396 -2.5 3.3 1.55 0.1272304553678157 -0.5 1.1 1.55 0.1232601687154404 0.5 1.1 1.55 2.329795466512829 2.5 3.3 1.55 3.389002026446801 -2.5 3.3 2.85 -0.1881951028251677 -0.5 1.1 2.85 -1.076420380654702 0.5 1.1 2.85 5.752182468090797 2.5 3.3 2.85 9.999856740330408 0.825 6.7 0.25 1.031720896431989 1.1 6.7 0.25 1.042486702924995 1.65 6.7 0.25 1.064311200094909 3.3 6.7 0.25 1.132184436974234 0.825 6.7 1.55 1.232840268856845 1.1 6.7 1.55 1.320065448202734 1.65 6.7 1.55 1.510481152231083 3.3 6.7 1.55 2.230752078594052 0.825 6.7 2.85 1.519728629818314 1.1 6.7 2.85 1.736493817025085 1.65 6.7 2.85 2.249233030766814 3.3 6.7 2.85 4.637773711917896 hyper_2f1_values_test(): hyper_2f1_values() stores values of the hypergeometric function 2F1 A B C X F -2 3 6.700000 0.250000 0.7235612934899779 0 1 6.700000 0.250000 0.9791110934527796 0 1 6.700000 0.250000 1.021657814008856 2 3 6.700000 0.250000 1.405156320011213 -2 3 6.700000 0.550000 0.4696143163982161 0 1 6.700000 0.550000 0.9529619497744632 0 1 6.700000 0.550000 1.051281421394799 2 3 6.700000 0.550000 2.399906290477786 -2 3 6.700000 0.850000 0.2910609592841472 0 1 6.700000 0.850000 0.9253696791037318 0 1 6.700000 0.850000 1.0865504094807 2 3 6.700000 0.850000 5.738156552618904 3 6 -5.500000 0.250000 15090.66974870461 1 6 -0.500000 0.250000 -104.3117006736435 1 6 0.500000 0.250000 21.17505070776881 3 6 4.500000 0.250000 4.194691581903192 3 6 -5.500000 0.550000 10170777974.04881 1 6 -0.500000 0.550000 -24708.63532248916 1 6 0.500000 0.550000 1372.230454838499 3 6 4.500000 0.550000 58.09272870639465 3 6 -5.500000 0.850000 5.868208761512417e+18 1 6 -0.500000 0.850000 -446350101.47296 1 6 0.500000 0.850000 5383505.756129573 3 6 4.500000 0.850000 20396.91377601966 hyper_2f1_complex_values_test(): hyper_2f1_complex_values() stores values of the hypergeometric function 2F1(a,b,c;z) A B C Z FZ 3 1 6.700000 (1.000000,0.000000) ( 5.469, 0) 3 -1 6.700000 (1.000000,0.000000) ( 0.337506, 0) -5 3 6.700000 (5.200000,4.800000) ( 116.827, 603.891) 3 -6 3.700000 (5.200000,-4.800000) ( 17620.4, 38293.8) -7 3 -3.700000 (5.200000,-4.800000) ( -1.17728e+10, -1.43823e+10) 4 -8 -3.700000 (5.200000,4.800000) ( 1.31612e+12, -1.01299e+11) 3 5 6.700000 (0.200000,0.100000) ( 1.73306, 0.63401) 3 -2 6.700000 (0.200000,0.500000) ( 0.647622, -0.521105) 3 4 6.700000 (0.800000,0.300000) ( -1.48301, 8.37443) 7 5 4.100000 (3.000000,-1.000000) ( -0.00403761, -0.00295663) 5 7 4.100000 (3.000000,-1.000000) ( -0.00403761, -0.00295663) 3 1 9.700000 (0.600000,0.900000) ( 1.03431, 0.544739) 2 5 9.700000 (0.500000,0.700000) ( 0.688504, 1.22742) 8 3 6.700000 (0.500000,0.700000) ( -0.900465, -1.11989) 8 2 6.700000 (0.600000,0.900000) ( -0.460839, -0.545757) hypergeometric_cdf_values: hypergeometric_cdf_values() stores values of the hypergeometric CDF. Sam Suc Pop X F 10 90 100 7 0.0600185817750058 10 90 100 8 0.2615284665839845 10 90 100 9 0.6695237889132748 10 90 100 10 1.0000000000000000 6 90 100 6 1.0000000000000000 7 90 100 6 0.5332595856827856 8 90 100 6 0.1819495964117640 9 90 100 6 0.0444804701752773 10 10 100 6 0.9999991751316731 10 30 100 6 0.9926860896560750 10 50 100 6 0.8410799901444538 10 70 100 6 0.3459800113391901 10 90 90 0 0.0000000000000000 10 90 200 0 0.0020888881396345 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 hypergeometric_pdf_values(): hypergeometric_pdf_values() stores values of the hypergeometric PDF. Sam Suc Pop X F 10 90 100 7 0.0517937053324283 10 90 100 8 0.2015098848089788 10 90 100 9 0.4079953223292903 10 90 100 10 0.3304762110867252 6 90 100 6 0.5223047493549779 7 90 100 6 0.3889503452643453 8 90 100 6 0.1505614239732950 9 90 100 6 0.0392768932104248 10 10 100 6 0.0000309982846552 10 30 100 6 0.0314511609393820 10 50 100 6 0.2114132170316862 10 70 100 6 0.2075776621999210 10 90 90 0 0.0000000000000000 10 90 200 0 0.0020888881396345 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 hypergeometric_u_values_test(): hypergeometric_u_values() stores values of the Hypergeometric U function. A B X F -2.500000 3.300000 0.250000 -68.69362872807861 -0.500000 1.100000 0.250000 -0.002971055137476107 0.500000 1.100000 0.250000 1.50086317421778 2.500000 3.300000 0.250000 20.6146882442006 -2.500000 3.300000 1.550000 7.456381546930555 -0.500000 1.100000 1.550000 1.015579376774929 0.500000 1.100000 1.550000 0.7344653893662267 2.500000 3.300000 1.550000 0.280464049418794 -2.500000 3.300000 2.850000 3.450815374144655 -0.500000 1.100000 2.850000 1.515663736875306 0.500000 1.100000 2.850000 0.56042118587935 2.500000 3.300000 2.850000 0.06489714773513422 0.825000 6.700000 0.250000 223432.0235697746 1.100000 6.700000 0.250000 263079.2598074081 1.650000 6.700000 0.250000 269802.9031935128 3.300000 6.700000 0.250000 82809.31133560656 0.825000 6.700000 1.550000 26.46568478313185 1.100000 6.700000 1.550000 28.09350617251606 1.650000 6.700000 1.550000 23.88916462451887 3.300000 6.700000 1.550000 4.533884785707039 0.825000 6.700000 2.850000 3.022446936269484 1.100000 6.700000 2.850000 2.804065091371336 1.650000 6.700000 2.850000 1.926257811148017 3.300000 6.700000 2.850000 0.2302051811586091 i0ml0_values_test(): i0ml0_values() stores values of the i0ml0() function. X i0ml0(X) 0.001953 0.9987575551546175 0.015625 0.9901135823070665 0.125000 0.9241943531002395 0.500000 0.7362426713471427 1.000000 0.5558226918141175 2.000000 0.3421515443446216 4.000000 0.1708717488877471 8.000000 0.0810810087092192 12.000000 0.0534494214410896 16.000000 0.0399503210089232 16.250000 0.0393306374375849 17.000000 0.0375822743428087 20.000000 0.0319124865544804 25.000000 0.0255061468835047 30.000000 0.0212444803178253 40.000000 0.0159254983485517 50.000000 0.0127375069272426 75.000000 0.0084897750814785 100.000000 0.0063668349178454 125.000000 0.0050932843163123 i1ml1_values_test(): i1ml1_values() stores values of the i1ml1() function. X i1ml1(X) 0.001953 0.0009757534615539 0.015625 0.0077609293280609 0.125000 0.0593029664045454 0.500000 0.2039521227673737 1.000000 0.3383947229366764 2.000000 0.4878770672696132 4.000000 0.5901873419657652 8.000000 0.6260453953031215 12.000000 0.6320931527490976 16.000000 0.6341017931323536 16.250000 0.6341796679757813 17.000000 0.6343926863239209 20.000000 0.6350157907325777 25.000000 0.6355961667735945 30.000000 0.6359100182669711 40.000000 0.6362211318175107 50.000000 0.6363648170213361 75.000000 0.6365065349961990 100.000000 0.6365560912630026 125.000000 0.6365790208718393 i4_fall_values_test(): i4_fall_values() returns values of the integer falling factorial. 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 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 values of the integer rising factorial. 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() stores values of the integer part function. X INT(X) -2.010000 -2.0000000000000000 -1.990000 -1.0000000000000000 -1.500000 -1.0000000000000000 -1.100000 -1.0000000000000000 -1.010000 -1.0000000000000000 -1.000000 -1.0000000000000000 -0.990000 0.0000000000000000 -0.900000 0.0000000000000000 -0.510000 0.0000000000000000 -0.500000 0.0000000000000000 -0.490000 0.0000000000000000 -0.010000 0.0000000000000000 0.000000 0.0000000000000000 0.010000 0.0000000000000000 0.490000 0.0000000000000000 0.500000 0.0000000000000000 0.510000 0.0000000000000000 0.900000 0.0000000000000000 0.990000 0.0000000000000000 1.000000 1.0000000000000000 1.010000 1.0000000000000000 1.100000 1.0000000000000000 1.500000 1.0000000000000000 1.990000 1.0000000000000000 2.010000 2.0000000000000000 inverse_chi_square_pdf_values_test(): inverse_chi_square_pdf_values() returns values of the inverse Chi Square Probability Density Function. DF X PDF 1 0.1 0.08500366602520341 2 0.1 0.3368973499542734 1 0.2 0.3661245640481622 2 0.2 1.026062482798735 1 0.4 0.4518059816704532 2 0.4 0.8953274901880941 3 0.4 1.129514954176133 4 0.4 1.119159362735118 1 1 0.2419707245191433 2 1 0.3032653298563167 3 1 0.2419707245191433 4 1 0.1516326649281584 5 1 0.08065690817304778 3 2 0.0549239111834653 3 3 0.02166329508030457 3 4 0.01100204146138436 3 5 0.006457369034861447 3 6 0.004162370481945731 10 1 0.0007897534631674914 10 2 1.584474249412852e-05 10 3 1.511920090468204e-06 inverse_gamma_pdf_values_test(): inverse_gamma_pdf_values() returns values of the inverse gamma Probability Density Function. ALPHA BETA X PDF 1 0.5 1 0.3032653298563167 1 0.5 2 0.09735009788392561 1 0.5 3 0.047026762493923 1 0.5 4 0.02757802820576861 1 2 2 0.1839397205857212 1 3 2 0.1673476201113224 1 4 2 0.1353352832366127 1 5 2 0.1026062482798735 2 2 3 0.07606179541223586 3 2 3 0.02535393180407862 4 2 3 0.005634207067573026 5 2 3 0.0009390345112621711 is_gaussian_prime_values_test(): is_gaussian_prime_values() stores values of the is_gaussian_prime() function. c is_gaussian_prime(c) (0,0) False (3,0) True (2,0) False (7,0) True (12,0) False (11,0) True (509,0) False (503,0) True (2,0) False (-5,-4) True (0,6) False (-4,-5) True (4,-3) False (-3,-2) True (-3,3) False (-2,-5) True (1,5) False (-1,-2) True (3,1) False (1,-4) True (0,1) False (2,-3) True (7,3) False (4,1) True is_prime_values_test(): is_prime_values() stores 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 145253029 True jacobi_cn_values_test(): jacobi_cn_values() stores values of the Jacobi CN function. U M jacobi_CN(U,M) 0.100000 0.000000 0.9950041652780258 0.200000 0.000000 0.9800665778412416 0.500000 0.000000 0.8775825618903726 1.000000 0.000000 0.5403023058681397 2.000000 0.000000 -0.4161468365471424 0.100000 0.500000 0.9950124626090582 0.200000 0.500000 0.9801976276784098 0.500000 0.500000 0.8822663948904403 1.000000 0.500000 0.5959765676721407 2.000000 0.500000 -0.1031836155277618 0.100000 1.000000 0.9950207489532265 0.200000 1.000000 0.9803279976447253 0.500000 1.000000 0.8868188839700739 1.000000 1.000000 0.6480542736638853 2.000000 1.000000 0.2658022288340797 4.000000 1.000000 0.03661899347368653 -0.200000 1.000000 0.9803279976447253 -0.500000 1.000000 0.8868188839700739 -1.000000 1.000000 0.6480542736638853 -2.000000 1.000000 0.2658022288340797 jacobi_dn_values_test(): jacobi_dn_values() stores values of the Jacobi dn() function. U M jacobi_DN(U,M) 0.100000 0.000000 1 0.200000 0.000000 1 0.500000 0.000000 1 1.000000 0.000000 1 2.000000 0.000000 1 0.100000 0.500000 0.9975093485144243 0.200000 0.500000 0.9901483195224799 0.500000 0.500000 0.9429724257773857 1.000000 0.500000 0.8231610016315963 2.000000 0.500000 0.7108610477840873 0.100000 1.000000 0.9950207489532265 0.200000 1.000000 0.9803279976447253 0.500000 1.000000 0.8868188839700739 1.000000 1.000000 0.6480542736638853 2.000000 1.000000 0.2658022288340797 4.000000 1.000000 0.03661899347368653 -0.200000 1.000000 0.9803279976447253 -0.500000 1.000000 0.8868188839700739 -1.000000 1.000000 0.6480542736638853 -2.000000 1.000000 0.2658022288340797 jacobi_poly_values_test(): jacobi_poly_values() stores values of the Jacobi polynomials. N A B X F 0 0.000000 1.000000 0.500000 1 1 0.000000 1.000000 0.500000 0.25 2 0.000000 1.000000 0.500000 -0.375 3 0.000000 1.000000 0.500000 -0.484375 4 0.000000 1.000000 0.500000 -0.1328125 5 0.000000 1.000000 0.500000 0.275390625 5 1.000000 1.000000 0.500000 -0.1640625 5 2.000000 1.000000 0.500000 -1.1748046875 5 3.000000 1.000000 0.500000 -2.361328125 5 4.000000 1.000000 0.500000 -2.6162109375 5 5.000000 1.000000 0.500000 0.1171875 5 0.000000 2.000000 0.500000 0.421875 5 0.000000 3.000000 0.500000 0.5048828125 5 0.000000 4.000000 0.500000 0.509765625 5 0.000000 5.000000 0.500000 0.4306640625 5 0.000000 1.000000 -1.000000 -6 5 0.000000 1.000000 -0.800000 0.03862 5 0.000000 1.000000 -0.600000 0.81184 5 0.000000 1.000000 -0.400000 0.03666 5 0.000000 1.000000 -0.200000 -0.48512 5 0.000000 1.000000 0.000000 -0.3125 5 0.000000 1.000000 0.200000 0.18912 5 0.000000 1.000000 0.400000 0.40234 5 0.000000 1.000000 0.600000 0.01216 5 0.000000 1.000000 0.800000 -0.43962 5 0.000000 1.000000 1.000000 1 jacobi_sn_values_test(): jacobi_sn_values() stores values of the Jacobi SN function. U M jacobi_SN(U,M) 0.100000 0.000000 0.09983341664682815 0.200000 0.000000 0.1986693307950612 0.500000 0.000000 0.479425538604203 1.000000 0.000000 0.8414709848078965 2.000000 0.000000 0.9092974268256817 0.100000 0.500000 0.09975068547462485 0.200000 0.500000 0.1980217429819704 0.500000 0.500000 0.4707504736556573 1.000000 0.500000 0.8030018248956439 2.000000 0.500000 0.9946623253580177 0.100000 1.000000 0.09966799462495582 0.200000 1.000000 0.197375320224904 0.500000 1.000000 0.4621171572600098 1.000000 1.000000 0.7615941559557649 2.000000 1.000000 0.9640275800758169 4.000000 1.000000 0.999329299739067 -0.200000 1.000000 -0.197375320224904 -0.500000 1.000000 -0.4621171572600098 -1.000000 1.000000 -0.7615941559557649 -2.000000 1.000000 -0.9640275800758169 jed_ce_values_test(): jed_ce_values stores of the YMDF CE calendar date for a given JED JED Y M D F 0.0 -4713 1 1 0.5 1.0 -4713 1 2 0.5 259261.0 -4004 10 26 0.5 347998.5 -3761 10 8 0 584282.5 -3114 9 6 0 588465.8 -3102 2 18 0.25 758325.5 -2637 3 8 0 1438178.5 -776 7 9 0 1446389.5 -753 1 1 0 1448637.5 -747 2 26 0 1448637.5 -747 2 26 0 1607708.5 -312 9 1 0 1607738.5 -312 10 1 0 1713262.5 -23 8 29 0 1721422.5 -1 12 31 0 1721423.5 1 1 1 0 1721425.5 1 1 3 0 1721425.5 1 1 3 0 1724220.5 8 8 29 0 1741959.5 57 3 24 0 1749994.5 79 3 24 0 1825029.5 284 8 29 0 1862836.5 388 3 3 0 1922867.5 552 7 11 0 1936747.5 590 7 12 0 1940351.5 600 5 24 0 1948320.5 622 3 19 0 1948438.5 622 7 15 0 1948439.5 622 7 16 0 1952062.5 632 6 16 0 1952067.5 632 6 21 0 2114872.5 1078 3 17 0 2289425.5 1556 2 9 0 2299160.0 1582 10 4 0.5 2299161.0 1582 10 15 0.5 2333269.5 1676 3 4 0 2361221.0 1752 9 13 0.5 2361222.0 1752 9 14 0.5 2372547.5 1783 9 18 0 2375839.5 1792 9 22 0 2394646.5 1844 3 21 0 2394710.5 1844 5 24 0 2400000.5 1858 11 17 0 2415020.3 1899 12 31 0.81 2440587.5 1970 1 1 0 2444244.5 1980 1 6 0 2450138.5 1996 2 25 0 2451544.5 2000 1 1 0 2453073.8 2004 3 9 0.33 2456284.5 2012 12 23 0 2913943.0 3266 1 1 0.5 jed_mjd_values_test(): jed_mjd_values() stores values of the Modified Julian Date. JED MJD(JED) 1507231.500000 -892769.0000000000000000 1660037.500000 -739963.0000000000000000 1746893.500000 -653107.0000000000000000 1770641.500000 -629359.0000000000000000 1892731.500000 -507269.0000000000000000 1931579.500000 -468421.0000000000000000 1974851.500000 -425149.0000000000000000 2091164.500000 -308836.0000000000000000 2121509.500000 -278491.0000000000000000 2155779.500000 -244221.0000000000000000 2174029.500000 -225971.0000000000000000 2191584.500000 -208416.0000000000000000 2195261.500000 -204739.0000000000000000 2229274.500000 -170726.0000000000000000 2245580.500000 -154420.0000000000000000 2266100.500000 -133900.0000000000000000 2288542.500000 -111458.0000000000000000 2290901.500000 -109099.0000000000000000 2323140.500000 -76860.0000000000000000 2334848.500000 -65152.0000000000000000 2348020.500000 -51980.0000000000000000 2366978.500000 -33022.0000000000000000 2385648.500000 -14352.0000000000000000 2392825.500000 -7175.0000000000000000 2416223.500000 16223.0000000000000000 2425848.500000 25848.0000000000000000 2430266.500000 30266.0000000000000000 2430833.500000 30833.0000000000000000 2431004.500000 31004.0000000000000000 2448698.500000 48698.0000000000000000 2450138.500000 50138.0000000000000000 2465737.500000 65737.0000000000000000 2486076.500000 86076.0000000000000000 jed_rd_values_test(): jed_rd_values() stores values of the Reingold Dershowitz Date. JED RD(JED) 1507231.500000 -214193.0000000000000000 1660037.500000 -61387.0000000000000000 1746893.500000 25469.0000000000000000 1770641.500000 49217.0000000000000000 1892731.500000 171307.0000000000000000 1931579.500000 210155.0000000000000000 1974851.500000 253427.0000000000000000 2091164.500000 369740.0000000000000000 2121509.500000 400085.0000000000000000 2155779.500000 434355.0000000000000000 2174029.500000 452605.0000000000000000 2191584.500000 470160.0000000000000000 2195261.500000 473837.0000000000000000 2229274.500000 507850.0000000000000000 2245580.500000 524156.0000000000000000 2266100.500000 544676.0000000000000000 2288542.500000 567118.0000000000000000 2290901.500000 569477.0000000000000000 2323140.500000 601716.0000000000000000 2334848.500000 613424.0000000000000000 2348020.500000 626596.0000000000000000 2366978.500000 645554.0000000000000000 2385648.500000 664224.0000000000000000 2392825.500000 671401.0000000000000000 2416223.500000 694799.0000000000000000 2425848.500000 704424.0000000000000000 2430266.500000 708842.0000000000000000 2430833.500000 709409.0000000000000000 2431004.500000 709580.0000000000000000 2448698.500000 727274.0000000000000000 2450138.500000 728714.0000000000000000 2465737.500000 744313.0000000000000000 2486076.500000 764652.0000000000000000 jed_weekday_values_test(): jed_weekday_values() stores values of the Weekday for a given JED. JED WEEKDAY(JED) 1507231.500000 1 1660037.500000 4 1746893.500000 4 1770641.500000 1 1892731.500000 4 1931579.500000 2 1974851.500000 7 2091164.500000 1 2121509.500000 1 2155779.500000 6 2174029.500000 7 2191584.500000 6 2195261.500000 1 2229274.500000 1 2245580.500000 4 2266100.500000 7 2288542.500000 7 2290901.500000 7 2323140.500000 4 2334848.500000 1 2348020.500000 6 2366978.500000 1 2385648.500000 2 2392825.500000 4 2416223.500000 1 2425848.500000 1 2430266.500000 2 2430833.500000 2 2431004.500000 5 2448698.500000 3 2450138.500000 1 2465737.500000 4 2486076.500000 1 kei0_values_test(): kei0_values() stores values of the Kelvin kei() function. of order 0. X kei(0,X) 0.000000 0 0.500000 -0.6715816950943676 1.000000 -0.4949946365187199 1.500000 -0.3313955623385585 2.000000 -0.2024000677647043 2.500000 -0.1106960991556749 3.000000 -0.05112188404598678 3.500000 -0.01600256851827124 4.000000 0.00219839929497252 4.500000 0.009720918540151989 5.000000 0.01118758650986964 kei1_values_test(): kei1_values() stores values of the Kelvin kei function of order 1. X kei(1,X) 0.500000 -1.051182085412523 1.000000 -0.2419959664297382 1.500000 0.001008680985009855 2.000000 0.08004939780706674 2.500000 0.0933137881353575 3.000000 0.08027022252392219 3.500000 0.05937625647622691 4.000000 0.03916601076917133 4.500000 0.0230021602469025 5.000000 0.01157775439325247 ker0_values_test(): ker0_values() stores values of the Kelvin ker() function. of order 0. X KER(0,X) 0.500000 0.8559058721186342 1.000000 0.286706208728316 1.500000 0.05293491548771044 2.000000 -0.04166451399150953 2.500000 -0.06968797258904534 3.000000 -0.0670292333037987 3.500000 -0.05263927724224119 4.000000 -0.03617884789954761 4.500000 -0.02199987504667382 5.000000 -0.01151172719949066 ker1_values_test(): ker1_values() stores values of the Kelvin ker() function of order 1. X KER(1,X) 0.500000 -1.52240340653209 1.000000 -0.7403222768419827 1.500000 -0.4170442851662574 2.000000 -0.230805929518123 2.500000 -0.1172561358598705 3.000000 -0.04989830778751491 3.500000 -0.01272324936181659 4.000000 0.005351296460277448 4.500000 0.01209090413515866 5.000000 0.01273739048421857 laguerre_associated_values_test(): laguerre_associated_values() stores values of the associated Laguerre function. N M X F 1 0 0.000000 1 2 0 0.000000 1 3 0 0.000000 1 4 0 0.000000 1 5 0 0.000000 1 1 1 0.500000 1.5 2 1 0.500000 1.625 3 1 0.500000 1.479166666666667 4 1 0.500000 1.1484375 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 56.2245364718967 7 3 0.250000 74.84729341779436 8 4 0.250000 323.8912982762806 9 4 0.250000 442.6100000097533 10 5 0.250000 1936.87657228825 laguerre_general_values_test(): laguerre_general_values() stores values of the general Laguerre function. N A X F 5 0.000000 0.250000 0.03726399739583333 5 0.250000 0.250000 0.3494791666666667 5 0.500000 0.250000 0.8710042317708333 5 0.750000 0.250000 1.672395833333333 5 1.500000 0.250000 6.657625325520833 5 2.500000 0.250000 23.95726725260417 5 5.000000 0.250000 203.1344319661458 8 1.200000 0.000000 12.841939968 8 1.200000 0.200000 5.359924801587302 8 1.200000 0.400000 0.9204589064126985 8 1.200000 0.600000 -1.341585114857143 8 1.200000 0.800000 -2.119726307555556 8 1.200000 1.000000 -1.959193658349206 0 5.200000 0.750000 1 1 5.200000 0.750000 5.45 2 5.200000 0.750000 17.20125 3 5.200000 0.750000 41.1039375 4 5.200000 0.750000 82.39745859375 5 5.200000 0.750000 146.0179186171875 6 5.200000 0.750000 235.9204608298828 laguerre_polynomial_values_test(): laguerre_polynomial_values() stores values of the Laguerre polynomials. N X L(N)(X) 0 1.000000 1.0000000000000000 1 1.000000 0.0000000000000000 2 1.000000 -0.5000000000000000 3 1.000000 -0.6666666666666667 4 1.000000 -0.6250000000000000 5 1.000000 -0.4666666666666667 6 1.000000 -0.2569444444444444 7 1.000000 -0.0404761904761905 8 1.000000 0.1539930555555556 9 1.000000 0.3097442680776014 10 1.000000 0.4189459325396825 11 1.000000 0.4801341790925124 12 1.000000 0.4962122235082305 5 0.500000 -0.4455729166666667 5 3.000000 0.8500000000000000 5 5.000000 -3.1666666666666670 5 10.000000 34.3333333333333286 lambert_w_values_test(): lambert_w_values() stores values of the Lambert W function. x branch lambert_w(x) -0.036788 -1 -4.8897201698674291 -0.073576 -1 -3.9943083470021219 -0.110364 -1 -3.4392164832802039 -0.147152 -1 -3.0223132453246571 -0.183940 -1 -2.6783469900166610 -0.220728 -1 -2.3764213420628870 -0.257516 -1 -2.0973492107034919 -0.294304 -1 -1.8243883090329840 -0.331091 -1 -1.5318116083896121 -0.367879 -1 -1.0000000000000000 -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 -0.073576 0 -0.0796781605114770 -0.036788 0 -0.0382212417467990 0.000000 0 0.0000000000000000 0.500000 0 0.3517337112491958 1.000000 0 0.5671432904097840 1.500000 0 0.7258613577662263 2.000000 0 0.8526055020137255 2.500000 0 0.9585863567287028 2.718282 0 1.0000000000000000 3.000000 0 1.0499088949640401 3.500000 0 1.1302893269741361 4.000000 0 1.2021678731970431 4.500000 0 1.2672378143074350 5.000000 0 1.3267246652422000 5.500000 0 1.3815453794450410 6.000000 0 1.4324047758983001 6.500000 0 1.4798568301738511 7.000000 0 1.5243452049841439 7.500000 0 1.5662309537823880 8.000000 0 1.6058119963201780 10.000000 0 1.7455280027406990 100.000000 0 3.3856301402900502 1000.000000 0 5.2496028524015959 1000000.000000 0 11.3833580861400492 laplace_cdf_values_test(): laplace_cdf_values() stores values of the Laplace CDF. Mu Beta X F(Mu,Beta,X) 0.000000 1.000000 0.000000 0.5 0.000000 1.000000 1.000000 0.8160602794142788 0.000000 1.000000 2.000000 0.9323323583816937 0.000000 1.000000 3.000000 0.975106465816068 0.000000 2.000000 1.000000 0.6967346701436833 0.000000 3.000000 1.000000 0.6417343447131054 0.000000 4.000000 1.000000 0.6105996084642976 0.000000 5.000000 1.000000 0.5906346234610091 1.000000 2.000000 1.000000 0.5 2.000000 2.000000 1.000000 0.3032653298563167 3.000000 2.000000 1.000000 0.1839397205857212 4.000000 2.000000 1.000000 0.1115650800742149 legendre_associated_values_test(): legendre_associated_values() stores values of the associated Legendre function. N M X F 1 0 0.000000 0 2 0 0.000000 -0.5 3 0 0.000000 0 4 0 0.000000 0.375 5 0 0.000000 0 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 -0.28 3 1 0.200000 1.175755076535925 3 2 0.200000 2.88 3 3 0.200000 -14.10906091843111 4 2 0.250000 -3.955078125 5 2 0.250000 -9.99755859375 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() stores values of the normalized associated Legendre function. N M X F 0 0 0.500000 0.7071067811865475 1 0 0.500000 0.6123724356957945 1 1 0.500000 -0.75 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 -0.566741212915553 legendre_associated_normalized_sphere_values_test(): legendre_associated_normalized_sphere_values() stores values of the associated Legendre function normalized for the surface of a sphere. N M X F 0 0 0.500000 0.2820947917738781 1 0 0.500000 0.24430125595146 1 1 0.500000 -0.2992067103010745 2 0 0.500000 -0.07884789131313 2 1 0.500000 -0.3345232717786446 2 2 0.500000 0.2897056515173922 3 0 0.500000 -0.326529291016351 3 1 0.500000 -0.06997056236064664 3 2 0.500000 0.3832445536624809 3 3 0.500000 -0.2709948227475519 4 0 0.500000 -0.24462907724141 4 1 0.500000 0.2560660384200185 4 2 0.500000 0.1881693403754876 4 3 0.500000 -0.4064922341213279 4 4 0.500000 0.2489246395003027 5 0 0.500000 0.0840580442633982 5 1 0.500000 0.3293793022891428 5 2 0.500000 -0.1588847984307093 5 3 0.500000 -0.2808712959945307 5 4 0.500000 0.4127948151484925 5 5 0.500000 -0.2260970318780046 legendre_function_q_values_test(): legendre_function_q_values() stores values of the Legendre Q function N X F 0 0.250000 0.2554128118829953 1 0.250000 -0.9361467970292512 2 0.250000 -0.4787614548274669 3 0.250000 0.4246139251747229 4 0.250000 0.5448396833845414 5 0.250000 -0.0945132826167347 6 0.250000 -0.4973516573531213 7 0.250000 -0.1499018843853194 8 0.250000 0.3649161918783626 9 0.250000 0.3055676545072885 10 0.250000 -0.1832799367995643 3 0.000000 0.6666666666666667 3 0.100000 0.626867202876333 3 0.200000 0.5099015515315237 3 0.300000 0.3232754180589764 3 0.400000 0.08026113738148187 3 0.500000 -0.1986547714794823 3 0.600000 -0.4828663183349136 3 0.700000 -0.7252886849144387 3 0.800000 -0.8454443502398846 3 0.900000 -0.6627096245052618 legendre_normalized_polynomial_values_test(): legendre_normalized_polynomial_values() stores values of the normalized Legendre polynomials. N X F 0 0.25 0.7071067811865475 1 0.25 0.3061862178478972 2 0.25 -0.642337649721702 3 0.25 -0.6284815141846855 4 0.25 0.3345637065282053 5 0.25 0.7967179601799685 6 0.25 0.06189376866246124 7 0.25 -0.766588850921089 8 0.25 -0.4444760242953344 9 0.25 0.5450094674858101 10 0.25 0.7167706229835538 3 0 0 3 0.1 -0.2759472322745781 3 0.2 -0.5238320341483518 3 0.3 -0.7155919752205163 3 0.4 -0.823164625090267 3 0.5 -0.8184875533567997 3 0.6 -0.6734983296193094 3 0.7 -0.360134523476992 3 0.8 0.1496662954709581 3 0.9 0.8839665576253438 3 1 1.870828693386971 legendre_polynomial_values_test(): legendre_polynomial_values() stores values of the Legendre polynomials. N X F 0 0.250000 1 1 0.250000 0.25 2 0.250000 -0.40625 3 0.250000 -0.3359375 4 0.250000 0.15771484375 5 0.250000 0.3397216796875 6 0.250000 0.0242767333984375 7 0.250000 -0.2799186706542969 8 0.250000 -0.1524540185928345 9 0.250000 0.1768244206905365 10 0.250000 0.2212002165615559 3 0.000000 0 3 0.100000 -0.1475 3 0.200000 -0.28 3 0.300000 -0.3825 3 0.400000 -0.44 3 0.500000 -0.4375 3 0.600000 -0.36 3 0.700000 -0.1925 3 0.800000 0.08 3 0.900000 0.4725 3 1.000000 1 legendre_shifted_polynomial_values_test(): legendre_shifted_polynomial_values() stores values of the shifted Legendre polynomials. N X F 0 0.625 1 1 0.625 0.25 2 0.625 -0.40625 3 0.625 -0.3359375 4 0.625 0.15771484375 5 0.625 0.3397216796875 6 0.625 0.0242767333984375 7 0.625 -0.2799186706542969 8 0.625 -0.1524540185928345 9 0.625 0.1768244206905365 10 0.625 0.2212002165615559 3 0.5 0 3 0.55 -0.1475 3 0.6 -0.28 3 0.65 -0.3825 3 0.7 -0.44 3 0.75 -0.4375 3 0.8 -0.36 3 0.85 -0.1925 3 0.9 0.08 3 0.95 0.4725 3 1 1 lerch_values_test(): lerch_values() stores values of the Lerch function. Z S A F 1.000000 2 0.000000 1.6449340668482260 1.000000 3 0.000000 1.2020569031595940 1.000000 10 0.000000 1.0009945751278180 0.500000 2 1.000000 1.1644810529300249 0.500000 3 1.000000 1.0744263872160800 0.500000 10 1.000000 1.0004926412120141 0.333333 2 2.000000 0.2959190697935714 0.333333 3 2.000000 0.1394507503935608 0.333333 10 2.000000 0.0009823175058446 0.100000 2 3.000000 0.1177910993911311 0.100000 3 3.000000 0.0386844792229896 0.100000 10 3.000000 0.0000170314961419 lobachevsky_values_test(): lobachevsky_values() stores values of the LOBACHEVSKY function. X LOBACHEVSKY(X) 0.001953 0.0000000012417639 0.007812 0.0000000794733448 0.031250 0.0000050867598186 0.125000 0.0003260309790121 0.500000 0.0213805368154082 1.000000 0.1875381690208383 1.500000 0.8305119997188365 2.000000 1.8854362426679034 2.500000 2.1315988986516410 3.000000 2.1771120185613428 4.000000 2.2921027921896653 5.000000 3.9137195028784495 6.000000 4.3513563983836425 7.000000 4.4200644968478189 10.000000 6.5656013133623832 15.000000 10.8255046615045991 20.000000 13.3655128554742273 30.000000 21.1310026856399595 50.000000 34.8382365894491173 100.000000 69.6570624378373964 lobatto_polynomial_values_test(): lobatto_polynomial_values() stores values of the completed Lobatto polynomials. N X Lo(N)(X) 1 0.250000 0.9375000000000000 2 0.250000 0.7031250000000000 3 0.250000 -0.9667968750000000 4 0.250000 -1.5014648437500000 5 0.250000 0.3639221191406250 6 0.250000 2.0019149780273442 7 0.250000 0.6597948074340820 8 0.250000 -1.9344413280487061 9 0.250000 -1.7699411138892169 10 0.250000 1.2152436655014749 3 -1.000000 0.0000000000000000 3 -0.900000 0.8692500000000000 3 -0.800000 1.1879999999999999 3 -0.700000 1.1092500000000001 3 -0.600000 0.7680000000000000 3 -0.500000 0.2812500000000000 3 -0.400000 -0.2520000000000000 3 -0.300000 -0.7507500000000000 3 -0.200000 -1.1519999999999999 3 -0.100000 -1.4107499999999999 3 0.000000 -1.5000000000000000 3 0.100000 -1.4107499999999999 3 0.200000 -1.1519999999999999 3 0.300000 -0.7507500000000000 3 0.400000 -0.2520000000000000 3 0.500000 0.2812500000000000 3 0.600000 0.7680000000000000 3 0.700000 1.1092500000000001 3 0.800000 1.1879999999999999 3 0.900000 0.8692500000000000 3 1.000000 0.0000000000000000 lobatto_polynomial_derivative_values_test(): lobatto_polynomial_derivative_values() stores derivatives of the completed Lobatto polynomials. N X Lo'(N)(X) 1 0.250000 -0.5000000000000000 2 0.250000 2.4375000000000000 3 0.250000 4.0312500000000000 4 0.250000 -3.1542968750000000 5 0.250000 -10.1916503906250000 6 0.250000 -1.0196228027343750 7 0.250000 15.6754455566406303 8 0.250000 10.9766893386840803 9 0.250000 -15.9141978621482796 10 0.250000 -24.3320238217711413 3 -1.000000 12.0000000000000000 3 -0.900000 5.6699999999999999 3 -0.800000 0.9600000000000000 3 -0.700000 -2.3100000000000001 3 -0.600000 -4.3200000000000003 3 -0.500000 -5.2500000000000000 3 -0.400000 -5.2800000000000002 3 -0.300000 -4.5899999999999999 3 -0.200000 -3.3599999999999999 3 -0.100000 -1.7700000000000000 3 0.000000 0.0000000000000000 3 0.100000 1.7700000000000000 3 0.200000 3.3599999999999999 3 0.300000 4.5899999999999999 3 0.400000 5.2800000000000002 3 0.500000 5.2500000000000000 3 0.600000 4.3200000000000003 3 0.700000 2.3100000000000001 3 0.800000 -0.9600000000000000 3 0.900000 -5.6699999999999999 3 1.000000 -12.0000000000000000 log_values_test(): log_values() stores values of the log() function. X LOG(X) 0.000010 -11.5129254649702286 0.010000 -4.6051701859880918 0.100000 -2.3025850929940459 0.200000 -1.6094379124341003 0.300000 -1.2039728043259359 0.400000 -0.9162907318741551 0.500000 -0.6931471805599453 0.600000 -0.5108256237659907 0.700000 -0.3566749439387324 0.800000 -0.2231435513142098 0.900000 -0.1053605156578263 1.000000 0.0000000000000000 2.000000 0.6931471805599453 3.000000 1.0986122886681098 3.141593 1.1447298858494002 5.000000 1.6094379124341003 10.000000 2.3025850929940459 20.000000 2.9957322735539909 100.000000 4.6051701859880918 123456789.000000 18.6314017661680182 log_normal_cdf_values_test(): log_normal_cdf_values() stores values of the log_normal CDF. Mu Sigma X F(Mu,Sigma,X) 1.000000 0.500000 1.000000 0.02275013194817921 1.000000 0.500000 2.000000 0.2697049307349095 1.000000 0.500000 3.000000 0.5781741008028732 1.000000 0.500000 4.000000 0.7801170895122241 1.000000 2.000000 2.000000 0.4390310097476894 1.000000 3.000000 2.000000 0.4592655190218048 1.000000 4.000000 2.000000 0.4694258497695908 1.000000 5.000000 2.000000 0.4755320473858733 2.000000 2.000000 3.000000 0.3261051056816658 3.000000 2.000000 3.000000 0.1708799040927608 4.000000 2.000000 3.000000 0.0734325635795206 5.000000 2.000000 3.000000 0.02554673736161761 log_series_cdf_values_test(): log_series_cdf_values() stores values of the log_series_cdf function. T N log_series_cdf(T,N) 0.100000 1 0.9491221581029903 0.111111 1 0.9433541128559735 0.125000 1 0.9361094611773272 0.142857 1 0.9267370278044118 0.166667 1 0.9141358246245129 0.200000 1 0.8962840235449100 0.250000 1 0.8690148741955517 0.333333 1 0.8221011541254772 0.500000 1 0.7213475204444817 0.666667 1 0.6068261510845583 0.750000 1 0.5410106403333613 0.800000 1 0.4970679476476894 0.833333 1 0.4650921887927060 0.857149 1 0.4404842934597863 0.875000 1 0.4207860535926143 0.888889 1 0.4045507673897055 0.900000 1 0.3908650337129266 0.990000 1 0.2149757685421097 0.990000 0 0.0000000000000000 0.990000 1 0.2149757685421097 0.990000 2 0.3213887739704539 0.990000 3 0.3916213575531612 0.990000 4 0.4437690508633213 0.990000 5 0.4850700239649681 0.990000 6 0.5191433267738267 0.990000 7 0.5480569580144867 0.990000 8 0.5731033910767085 0.990000 9 0.5951442521714636 0.990000 10 0.6147826594068904 log10_values_test(): log10_values() stores values of the log10 function. X log10(X) 0.000010 -5.0000000000000000 0.010000 -2.0000000000000000 0.100000 -1.0000000000000000 0.200000 -0.6989700043360189 0.300000 -0.5228787452803375 0.400000 -0.3979400086720376 0.500000 -0.3010299956639812 0.600000 -0.2218487496163564 0.700000 -0.1549019599857432 0.800000 -0.0969100130080564 0.900000 -0.0457574905606751 1.000000 0.0000000000000000 2.000000 0.3010299956639812 3.000000 0.4771212547196624 3.141593 0.4971498726941339 5.000000 0.6989700043360189 10.000000 1.0000000000000000 20.000000 1.3010299956639813 100.000000 2.0000000000000000 123456789.000000 8.0915149771692700 logarithmic_integral_values_test(): logarithmic_integral_values() stores values of the logarithmic_integral function. X logarithmic_integral(X) 0.000000 0.0000000000000000 0.100000 -0.0323897895932910 0.200000 -0.0851264867287941 0.300000 -0.1574149028946895 0.400000 -0.2529494192126213 0.500000 -0.3786710430610880 0.600000 -0.5468514142104171 0.700000 -0.7809468775455607 0.800000 -1.1340119573823271 0.900000 -1.7758006834235249 0.950000 -2.4436225538732250 0.975000 -3.1241900505072109 1.031250 -2.8729355103291199 1.062500 -2.1642825241382071 1.125000 -1.4403512962794081 1.250000 -0.6864884538258716 1.500000 0.1250649863152964 2.000000 1.0451637801174929 4.000000 2.9675850950390510 8.000000 5.2537182995589307 16.000000 8.5197164637110596 32.000000 13.6050921770917199 64.000000 21.9346683280510000 128.000000 36.0425483172294392 256.000000 60.5130653379173324 512.000000 103.7211171690372993 1024.000000 181.0780396816944915 2048.000000 321.1144156746836984 logistic_cdf_values_test(): logistic_cdf_values() stores values of the Logistic CDF. Mu Beta X F(Mu,Beta,X) 1.000000 0.500000 1.000000 0.5 1.000000 0.500000 2.000000 0.8807970779778824 1.000000 0.500000 3.000000 0.9820137900379085 1.000000 0.500000 4.000000 0.9975273768433652 1.000000 2.000000 2.000000 0.6224593312018546 1.000000 3.000000 2.000000 0.5825702064623147 1.000000 4.000000 2.000000 0.5621765008857981 1.000000 5.000000 2.000000 0.549833997312478 2.000000 2.000000 3.000000 0.6224593312018546 3.000000 2.000000 3.000000 0.5 4.000000 2.000000 3.000000 0.3775406687981454 5.000000 2.000000 3.000000 0.2689414213699951 mcnugget_number_values_test(): mcnugget_number_values() stores values of the McNugget number. 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() stores indices of the 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() stores values of the MERTENS function. N MERTENS(N) 1 1 2 0 3 -1 4 -1 5 -2 6 -1 7 -2 8 -2 9 -2 10 -1 11 -2 12 -2 100 1 1000 2 10000 -23 mittag_leffler_ea_values_test(): mittag_leffler_ea_values() stores values of the Mittag-Leffler one parameter function E(A;X). A X E(A;X) 0.250000 0.000000 1 0.250000 -2.500000 0.2525646348870172 0.250000 -5.000000 0.1427989464258737 0.250000 -7.500000 0.0994231091392936 0.250000 -10.000000 0.0762370352397216 1.750000 0.000000 1 1.750000 -12.500000 -0.2579027070618285 1.750000 -25.000000 0.2716853059670252 1.750000 -37.500000 0.01846579916604009 1.750000 -50.000000 -0.139707389642194 2.250000 0.000000 1 2.250000 -25.000000 -1.022121843823497 2.250000 -50.000000 1.860844522589611 2.250000 -75.000000 2.644615445996891 2.250000 -100.000000 0.7762512036620307 1.000000 -5.000000 0.006737946999045729 2.000000 -5.000000 -0.6172728764571668 3.000000 -5.000000 0.2010457248089053 4.000000 -5.000000 0.7922864454196143 5.000000 -5.000000 0.958340222567225 6.000000 -5.000000 0.993055607747429 7.000000 -5.000000 0.999007936794713 8.000000 -5.000000 0.999875992064687 9.000000 -5.000000 0.999986221340384 10.000000 -5.000000 0.999998622134038 moebius_values_test(): moebius_values() stores values of the MOEBIUS function. N MOEBIUS(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 resturns some 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() 0 0.7000 2 1 0.3000 1 3 2 0.441 0 0.7000 2 1 0.3000 2 4 2 0.2646 0 0.5000 2 1 0.5000 1 3 2 0.375 0 0.6000 1 1 0.0000 1 2 0.4000 1 3 3 0 0 0.6000 3 1 0.1000 0 2 0.1000 0 3 0.1000 0 4 0.1000 0 3 5 0.216 0 0.6000 2 1 0.1000 1 2 0.1000 0 3 0.1000 0 4 0.1000 0 3 5 0.108 0 0.6000 1 1 0.1000 0 2 0.1000 2 3 0.1000 0 4 0.1000 0 3 5 0.018 0 0.6000 1 1 0.1000 0 2 0.1000 0 3 0.1000 1 4 0.1000 1 3 5 0.036 0 0.6000 0 1 0.1000 0 2 0.1000 0 3 0.1000 3 4 0.1000 0 3 5 0.001 0 0.6000 0 1 0.1000 1 2 0.1000 1 3 0.1000 1 4 0.1000 0 3 5 0.006 negative_binomial_cdf_values_test(): negative_binomial_cdf_values() stores values of the unit normal CDF. F S P CDF() 4 4 0.500000 0.6367187500000000 3 5 0.500000 0.3632812500000000 2 6 0.500000 0.1445312500000000 3 4 0.500000 0.5000000000000000 2 5 0.500000 0.2265625000000000 1 6 0.500000 0.0625000000000000 2 4 0.500000 0.3437500000000000 1 5 0.500000 0.1093750000000000 0 6 0.500000 0.0156250000000000 2 4 0.400000 0.1792000000000000 1 5 0.400000 0.0409600000000000 0 6 0.400000 0.0040960000000000 2 4 0.300000 0.0704700000000000 1 5 0.300000 0.0109350000000000 0 6 0.300000 0.0007290000000000 11 1 0.300000 0.9861587127990000 10 2 0.300000 0.9149749500510000 9 3 0.300000 0.7471846521450000 17 1 0.100000 0.8499053647030009 16 2 0.100000 0.5497160941090026 15 3 0.100000 0.2662040052146710 9 1 0.100000 0.6513215599000000 8 2 0.100000 0.2639010709000000 7 3 0.100000 0.0701908264000000 2 0 0.010000 1.0000000000000000 1 1 0.010000 0.0199000000000000 0 2 0.010000 0.0001000000000000 nine_j_values_test(): nine_j_values() stores values of the nine_j function. J1 J2 J3 J4 J5 J6 J7 J8 J9 nine_j(X) 1.0 8.0 7.0 6.5 7.5 7.5 6.0 10.0 6.0 0.0004270039294528 1.5 8.0 7.0 6.5 7.5 7.5 6.0 10.0 6.0 -0.0012289154510585 2.0 8.0 7.0 6.5 7.5 7.5 6.0 10.0 6.0 -0.0001944260688401 1.0 3.0 2.0 4.0 1.5 3.0 3.5 2.0 2.0 0.0033384199238856 1.5 3.0 2.0 4.0 1.5 3.0 3.5 2.0 2.0 -0.0007958936865080 2.0 3.0 2.0 4.0 1.5 3.0 3.5 2.0 2.0 -0.0043382086902520 0.5 0.5 1.0 2.0 1.0 1.5 1.5 0.5 1.5 0.0537914353639919 1.0 0.5 1.0 2.0 1.0 1.5 1.5 0.5 1.5 0.0062112999374994 1.5 0.5 1.0 2.0 1.0 1.5 1.5 0.5 1.5 0.0304290309725092 normal_01_cdf_values_test(): normal_01_cdf_values() stores values of the unit normal CDF. X normal_01_cdf(X) 0.000000 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 1.000000 0.8413447460685429 1.500000 0.9331927987311419 2.000000 0.9772498680518208 2.500000 0.9937903346742240 3.000000 0.9986501019683699 3.500000 0.9997673709209645 4.000000 0.9999683287581669 normal_cdf_values_test(): normal_cdf_values() stores values of the normal CDF. MU SIGMA X normal_cdf(X) 1.000000 0.500000 1.000000 0.5000000000000000 1.000000 0.500000 2.000000 0.9772498680518208 1.000000 0.500000 3.000000 0.9999683287581669 1.000000 0.500000 4.000000 0.9999999990134124 1.000000 2.000000 2.000000 0.6914624612740131 1.000000 3.000000 2.000000 0.6305586598182364 1.000000 4.000000 2.000000 0.5987063256829237 1.000000 5.000000 2.000000 0.5792597094391030 2.000000 2.000000 3.000000 0.6914624612740131 3.000000 2.000000 3.000000 0.5000000000000000 4.000000 2.000000 3.000000 0.3085375387259869 5.000000 2.000000 3.000000 0.1586552539314571 normal_pdf_values_test(): normal_pdf_values() stores values of the normal PDF. MU SIGMA X PDF -56.316341 4.785956 -46.854240 0.0118077593721326 12.339089 2.135005 6.781057 0.0063078491744789 -48.484442 0.638788 -50.232822 0.0147514774470322 26.793142 0.402463 26.671290 0.9468437743011001 -19.738744 3.797900 -12.964347 0.0214031229994179 -99.632326 4.497770 -103.660016 0.0593995996735349 -81.091050 0.166723 -80.731832 0.2348929157422787 68.169490 0.703209 66.091559 0.0072075156785713 -47.939400 4.571170 -58.535445 0.0059443968976567 -29.674268 4.132148 -35.447731 0.0363766316577132 omega_values_test(): omega_values() stores values of the OMEGA function. N OMEGA(N) 1 0 2 1 3 1 4 1 5 1 6 2 7 1 8 1 9 1 10 2 30 3 101 1 210 4 1320 4 1764 3 2003 1 2310 5 2827 2 8717 2 12553 1 30030 6 510510 7 9699690 8 owen_values_test(): owen_values() stores values of the OWEN function. H A T 0.062500 0.250000 0.038912 6.500000 0.437500 0.000000 7.000000 0.968750 0.000000 4.781250 0.062500 0.000000 2.000000 0.500000 0.008625 1.000000 0.999997 0.066742 1.000000 0.500000 0.043065 1.000000 1.000000 0.066742 1.000000 2.000000 0.078468 1.000000 3.000000 0.079300 0.500000 0.500000 0.064489 0.500000 1.000000 0.106671 0.500000 2.000000 0.141581 0.500000 3.000000 0.151084 0.250000 0.500000 0.071347 0.250000 1.000000 0.120129 0.250000 2.000000 0.166613 0.250000 3.000000 0.184750 0.125000 0.500000 0.073173 0.125000 1.000000 0.123763 0.125000 2.000000 0.173744 0.125000 3.000000 0.195119 0.007812 0.500000 0.073789 0.007812 1.000000 0.124995 0.007812 2.000000 0.176198 0.007812 3.000000 0.198777 0.007812 10.000000 0.234089 0.007812 100.000000 0.247946 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 partition count function for distinct parts N P(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() stores 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() stores 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() stores values of the Poisson CDF. A X FX 0.020000 0.000000 0.9801986733067553 0.100000 0.000000 0.9048374180359596 0.100000 1.000000 0.9953211598395555 0.500000 0.000000 0.6065306597126334 0.500000 1.000000 0.9097959895689501 0.500000 2.000000 0.9856123220330293 1.000000 0.000000 0.3678794411714423 1.000000 1.000000 0.7357588823428846 1.000000 2.000000 0.9196986029286058 1.000000 3.000000 0.9810118431238462 2.000000 0.000000 0.1353352832366127 2.000000 1.000000 0.4060058497098381 2.000000 2.000000 0.6766764161830635 2.000000 3.000000 0.857123460498547 5.000000 0.000000 0.006737946999085467 5.000000 1.000000 0.0404276819945128 5.000000 2.000000 0.1246520194830811 5.000000 3.000000 0.2650259152973617 5.000000 4.000000 0.4404932850652124 5.000000 5.000000 0.6159606548330631 5.000000 6.000000 0.7621834629729387 polylogarithm_values_test(): polylogarithm_values() stores values of the polylogarithm function. N Z F 2 1.000000 1.644934066848226 3 1.000000 1.202056903159594 10 1.000000 1.000994575127818 2 0.500000 0.5822405264650125 3 0.500000 0.5372131936080402 10 0.500000 0.5002463206060068 2 0.333333 0.3662132299770635 3 0.333333 0.3488278611548401 10 0.333333 0.3334424797228716 2 0.100000 0.1026177910993911 3 0.100000 0.101288684479223 10 0.100000 0.1000097826564961 polynomial_resultant_values_test(): polynomial_resultant_values() returns values of the resultant R of polynomials P and Q. P(x): 1 Q(x): 2 R: 1 P(x): 3 * x + 3 Q(x): 1 * x^2 + 2 * x + 1 R: 0 P(x): 1 * x^3 + 3 * x^2 + 3 * x + 1 Q(x): 1 * x^2 - 1 R: 0 P(x): 1 * x^3 + 2 * x^2 + 3 * x + 4 Q(x): 5 * x^2 + 6 * x + 7 R: 832 P(x): 1 * x^3 + 2 * x^2 + 3 * x + 4 Q(x): 4 * x^3 + 3 * x^2 + 2 * x + 1 R: -2000 P(x): 1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x Q(x): 1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x + 1 R: 1 P(x): 1 * x^4 - 4 * x^3 + 5 * x^2 - 2 * x Q(x): 1 * x^7 - 12 * x^6 + 60 * x^5 - 160 * x^4 + 240 * x^3 - 192 * x^2 + 64 * x R: 0 P(x): 2 * x^4 + 3 * x^3 + 4 * x^2 + 5 * x + 6 Q(x): 7 * x^3 + 8 * x^2 + 9 * x + 10 R: 204496 polyomino_chiral_count_values_test(): polyomino_chiral_count_values() returns counts of the number of chiral polyominoes. Order Number 0 1 1 1 2 1 3 2 4 7 5 18 6 60 7 196 8 704 9 2500 10 9189 11 33896 12 126759 13 476270 14 1802312 15 6849777 16 26152418 17 100203194 18 385221143 19 1485200848 20 5741256764 21 22245940545 22 86383382827 23 336093325058 24 1309998125640 25 5114451441106 26 19998172734786 27 78306011677182 28 307022182222506 29 1205243866707468 30 4736694001644862 polyomino_fixed_count_values_test(): polyomino_fixed_count_values() returns counts of the number of fixed polyominoes. Order Number 0 1 1 1 2 2 3 6 4 19 5 63 6 216 7 760 8 2725 9 9910 10 36446 11 135268 12 505861 13 1903890 14 7204874 15 27394666 16 104592937 17 400795844 18 1540820542 19 5940738676 20 22964779660 21 88983512783 22 345532572678 23 1344372335524 24 5239988770268 25 20457802016011 26 79992676367108 27 313224032098244 28 1228088671826973 polyomino_free_count_values_test(): polyomino_free_count_values() returns counts of the number of free polyominoes. Order Number 0 1 1 1 2 1 3 2 4 5 5 12 6 35 7 108 8 369 9 1285 10 4655 11 17073 12 63600 13 238591 14 901971 15 3426576 16 13079255 17 50107909 18 192622052 19 742624232 20 2870671950 21 11123060678 22 43191857688 23 168047007728 24 654999700403 25 2557227044764 26 9999088822075 27 39153010938487 28 153511100594603 prandtl_values_test(): prandtl_values() stores values of the PRANDTL function. TC P PRANDTL(TC.P) 0.000000 1.000000 13.5000000000000000 0.000000 5.000000 13.4800000000000004 0.000000 10.000000 13.4600000000000009 0.000000 25.000000 13.3900000000000006 0.000000 50.000000 13.2699999999999996 0.000000 75.000000 13.1500000000000004 0.000000 100.000000 13.0399999999999991 0.000000 125.000000 12.9299999999999997 0.000000 150.000000 12.8300000000000001 0.000000 175.000000 12.7300000000000004 0.000000 200.000000 12.6300000000000008 0.000000 225.000000 12.5299999999999994 0.000000 250.000000 12.4299999999999997 0.000000 275.000000 12.3399999999999999 0.000000 300.000000 12.2500000000000000 0.000000 350.000000 12.0800000000000001 0.000000 400.000000 11.9199999999999999 0.000000 450.000000 11.7699999999999996 0.000000 500.000000 11.6199999999999992 0.000000 550.000000 11.4800000000000004 0.000000 600.000000 11.3599999999999994 0.000000 650.000000 11.2300000000000004 0.000000 700.000000 11.1199999999999992 0.000000 800.000000 10.9100000000000001 0.000000 900.000000 10.7200000000000006 0.000000 1000.000000 10.5500000000000007 25.000000 1.000000 6.1369999999999996 50.000000 1.000000 3.5550000000000002 75.000000 1.000000 2.3780000000000001 100.000000 1.000000 1.0000000000000000 150.000000 1.000000 0.9740000000000000 200.000000 1.000000 0.9600000000000000 400.000000 1.000000 0.9240000000000000 600.000000 1.000000 0.8990000000000000 800.000000 1.000000 0.8820000000000000 prime_values_test(): prime_values() stores values of the PRIME function. N PRIME(N) 1 2 2 3 4 7 8 19 16 53 32 131 64 311 128 719 256 1619 512 3671 1000 7919 2000 17389 4000 37813 8000 81799 16000 176081 32000 376127 64000 800573 128000 1698077 256000 3588941 512000 7559173 1024000 15881419 2048000 33283031 4096000 69600977 8192000 145253029 psat_values_test(): psat_values() stores values of the PSAT function. TC P 0.010000 0.0061173000000000 1.000000 0.0065716000000000 5.000000 0.0087260000000000 50.000000 0.1234400000000000 100.000000 1.0132000000000001 125.000000 2.3201000000000001 150.000000 4.7572000000000001 200.000000 15.5370000000000008 250.000000 39.7370000000000019 300.000000 85.8379999999999939 350.000000 165.2100000000000080 373.976000 220.5500000000000114 psi_values_test(): psi_values() stores values of the psi() function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 r8_factorial_values_test(): r8_factorial_values() returns values of the real factorial function. N r8_factorial(N) 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288e+06 11 3.99168e+07 12 4.79002e+08 13 6.22702e+09 14 8.71783e+10 15 1.30767e+12 16 2.09228e+13 17 3.55687e+14 18 6.40237e+15 19 1.21645e+17 20 2.4329e+18 25 1.55112e+25 50 3.04141e+64 100 9.33262e+157 150 5.71338e+262 r8_factorial_log_values_test(): r8_factorial_log_values() returns values of the log factorial function. N r8_factorial_log(N) 0 0 1 0 2 0.693147 3 1.79176 4 3.17805 5 4.78749 6 6.57925 7 8.52516 8 10.6046 9 12.8018 10 15.1044 11 17.5023 12 19.9872 13 22.5522 14 25.1912 15 27.8993 16 30.6719 17 33.5051 18 36.3954 19 39.3399 20 42.3356 25 58.0036 50 148.478 100 363.739 150 605.02 500 2611.33 1000 5912.13 r8_factorial2_values_test(): r8_factorial2_values() returns values of the double factorial function. N N!! 0 1 1 1 2 2 3 3 4 8 5 15 6 48 7 105 8 384 9 945 10 3840 11 10395 12 46080 13 135135 14 645120 15 2.02702e+06 r8_fall_values_test(): r8_fall_values() returns values of the falling factorial. X N r8_fall(X,N) 5.0000 4 120 5.2500 4 163.16015625 5.5000 4 216.5625 5.7500 4 281.66015625 6.0000 4 360 7.5000 0 1 7.5000 1 7.5 7.5000 2 48.75 7.5000 3 268.125 7.5000 4 1206.5625 7.5000 5 4222.96875 7.5000 6 10557.421875 7.5000 7 15836.1328125 7.5000 8 7918.06640625 7.5000 9 -3959.033203125 r8_rise_values_test(): r8_rise_values() returns values of the rising factorial. X N r8_rise(X,N) 5.0000 4 1680 5.2500 4 1962.59765625 5.5000 4 2279.0625 5.7500 4 2631.97265625 6.0000 4 3024 7.5000 0 1 7.5000 1 7.5 7.5000 2 63.75 7.5000 3 605.625 7.5000 4 6359.0625 7.5000 5 73129.21875 7.5000 6 914115.234375 7.5000 7 12340555.6640625 7.5000 8 178938057.1289063 7.5000 9 2773539885.498047 rayleigh_cdf_values_test(): rayleigh_cdf_values() stores values of the Rayleigh CDF. SIGMA X rayleigh_cdf(SIGMA,X) 0.500000 1.000000 0.8646647167633873 0.500000 2.000000 0.9996645373720975 0.500000 3.000000 0.9999999847700203 0.500000 4.000000 0.999999999999987 1.000000 2.000000 0.8646647167633873 2.000000 2.000000 0.3934693402873666 3.000000 2.000000 0.199262597083192 4.000000 2.000000 0.1175030974154046 5.000000 2.000000 0.07688365361336422 scaled_inverse_chi_square_pdf_values_test(): scaled_inverse_chi_square_pdf_values() returns values of the scaled inverse Chi Square Probability Density Function. DF XI X PDF 1 0.5 0.1 0.7322491280963244 2 0.5 0.1 0.3368973499542734 1 0.5 0.2 0.9036119633409063 2 0.5 0.2 1.026062482798735 1 0.5 0.4 0.5968580144169457 2 0.5 0.4 0.8953274901880941 1 1 0.1 0.08500366602520341 2 1 0.1 0.004539992976248485 1 1 0.2 0.3661245640481622 2 1 0.2 0.1684486749771367 1 1 0.4 0.4518059816704532 2 1 0.4 0.5130312413993675 1 2 0.1 0.0008099910956089117 2 2 0.1 4.122307244877116e-07 1 2 0.2 0.04250183301260171 2 2 0.2 0.002269996488124243 1 2 0.4 0.1830622820240811 2 2 0.4 0.08422433748856833 secvir_values_test(): secvir_values() stores values of the second virial function. TC VIR 0.000000 -98.9599999999999937 5.000000 -90.0799999999999983 10.000000 -82.2900000000000063 20.000000 -69.3599999999999994 30.000000 -59.1899999999999977 40.000000 -51.0700000000000003 60.000000 -39.1300000000000026 90.000000 -27.8099999999999987 120.000000 -20.8299999999999983 150.000000 -16.2100000000000009 180.000000 -12.9800000000000004 210.000000 -10.6300000000000008 240.000000 -8.8499999999999996 300.000000 -6.3899999999999997 400.000000 -4.0300000000000002 500.000000 -2.7100000000000000 700.000000 -1.3200000000000001 1000.000000 -0.3900000000000000 2000.000000 0.5300000000000000 shi_values_test(): shi_values() stores values of the shi() function. X SHI(X) 0.500000 0.5069967498196672 0.600000 0.6121303965633808 0.700000 0.7193380189288998 0.800000 0.8289965633789345 0.900000 0.9414978265114335 1.000000 1.0572508753757290 1.200000 1.3002503610220570 1.400000 1.5617133883610019 1.600000 1.8458141413585041 1.800000 2.1572903434259012 2.000000 2.5015674333549760 2.500000 3.5493404062244349 3.000000 4.9734404758598068 3.500000 6.9661620675049418 4.000000 9.8173269112330335 4.500000 13.9678850493471494 si_values_test(): si_values() stores values of the SI function. X SI(X) 0.500000 0.4931074180430667 0.600000 0.5881288096080801 0.700000 0.6812222391166113 0.800000 0.7720957854819966 0.900000 0.8604707107452929 1.000000 0.9460830703671830 1.200000 1.1080471990137191 1.400000 1.2562267327792180 1.600000 1.3891804858704380 1.800000 1.5058167802555791 2.000000 1.6054129768026950 2.500000 1.7785201734438270 3.000000 1.8486525279994681 3.500000 1.8331253986659970 4.000000 1.7582031389490529 4.500000 1.6541404143792440 sigma_values_test(): sigma_values() stores values of the sigma() function. N SIGMA(N) 1 1 2 3 3 4 4 7 5 6 6 12 7 8 8 15 9 13 10 18 30 72 127 128 128 255 129 176 210 576 360 1170 617 618 815 984 816 2232 1000 2340 sin_values_test(): sin_values() stores values of the sine function. X SIN(X) 0.000000 0.0000000000000000 0.261799 0.2588190451025207 0.500000 0.4794255386042030 0.523599 0.5000000000000000 0.785398 0.7071067811865476 1.000000 0.8414709848078965 1.047198 0.8660254037844386 1.570796 1.0000000000000000 2.000000 0.9092974268256817 3.000000 0.1411200080598672 3.141593 0.0000000000000000 4.000000 -0.7568024953079282 5.000000 -0.9589242746631385 sin_degree_values_test(): sin_degree_values() stores values of the SIN function for degrees. X SIN(X) -5.000000 -0.0871557427476582 0.000000 0.0000000000000000 1.000000 0.0174524064372835 2.000000 0.0348994967025010 3.000000 0.0523359562429438 4.000000 0.0697564737441253 5.000000 0.0871557427476582 10.000000 0.1736481776669304 15.000000 0.2588190451025207 30.000000 0.5000000000000000 45.000000 0.7071067811865476 60.000000 0.8660254037844386 75.000000 0.9659258262890683 85.000000 0.9961946980917455 86.000000 0.9975640502598242 87.000000 0.9986295347545738 88.000000 0.9993908270190958 89.000000 0.9998476951563913 90.000000 1.0000000000000000 91.000000 0.9998476951563913 105.000000 0.9659258262890683 180.000000 0.0000000000000000 sin_power_int_values_test(): sin_power_int_values() stores values of the sine power integral. A B N F 10.000000 20.000000 0 10 0.000000 1.000000 1 0.4596976941318603 0.000000 1.000000 2 0.2726756432935796 0.000000 1.000000 3 0.1789405625488581 0.000000 1.000000 4 0.1240255653152068 0.000000 1.000000 5 0.08897439645157594 0.000000 2.000000 5 0.9039312384814995 1.000000 2.000000 5 0.8149568420299235 0.000000 1.000000 10 0.02188752242172985 0.000000 1.000000 11 0.01702343937406933 sinh_values_test(): sinh_values() stores values of the SINH function. X SINH(X) -5.000000 -74.2032105777887523 -1.000000 -1.1752011936438014 0.000000 0.0000000000000000 0.100000 0.1001667500198440 0.200000 0.2013360025410940 0.300000 0.3045202934471426 0.400000 0.4107523258028155 0.500000 0.5210953054937474 0.600000 0.6366535821482413 0.700000 0.7585837018395335 0.800000 0.8881059821876230 0.900000 1.0265167257081753 1.000000 1.1752011936438014 2.000000 3.6268604078470186 3.000000 10.0178749274099026 4.000000 27.2899171971277532 5.000000 74.2032105777887523 10.000000 11013.2328747033934633 six_j_values_test(): six_j_values() stores values of the six_j function. J1 J2 J3 J4 J5 J6 six_j(X) 1.0 8.0 7.0 6.5 7.5 7.5 0.0349090513837330 2.0 8.0 7.0 6.5 7.5 7.5 -0.0374302503965979 3.0 8.0 7.0 6.5 7.5 7.5 0.0189086639095956 4.0 8.0 7.0 6.5 7.5 7.5 0.0073424482549286 5.0 8.0 7.0 6.5 7.5 7.5 -0.0235893518508179 6.0 8.0 7.0 6.5 7.5 7.5 0.0191347695521544 7.0 8.0 7.0 6.5 7.5 7.5 0.0012880173977242 8.0 8.0 7.0 6.5 7.5 7.5 -0.0193001836629053 9.0 8.0 7.0 6.5 7.5 7.5 0.0167730594938289 10.0 8.0 7.0 6.5 7.5 7.5 0.0055011472748509 11.0 8.0 7.0 6.5 7.5 7.5 -0.0213543979089683 12.0 8.0 7.0 6.5 7.5 7.5 0.0034603644514354 13.0 8.0 7.0 6.5 7.5 7.5 0.0252095005479559 14.0 8.0 7.0 6.5 7.5 7.5 0.0148399056122171 15.0 8.0 7.0 6.5 7.5 7.5 0.0027085776806332 sound_values_test(): sound_values() stores values of the speed of sound function. TC P SOUND(TC.P) 0.000000 1.000000 1401.0000000000000000 100.000000 1.000000 472.8000000000000114 200.000000 1.000000 533.7000000000000455 300.000000 1.000000 585.7000000000000455 350.000000 1.000000 609.5000000000000000 400.000000 1.000000 632.2000000000000455 500.000000 1.000000 674.6000000000000227 600.000000 1.000000 713.8999999999999773 850.000000 1.000000 802.0000000000000000 1100.000000 1.000000 880.1000000000000227 1600.000000 1.000000 1017.7999999999999545 2000.000000 1.000000 1115.9000000000000909 0.000000 5.000000 1401.7000000000000455 0.000000 10.000000 1402.5999999999999091 0.000000 50.000000 1409.5999999999999091 0.000000 100.000000 1418.0999999999999091 0.000000 250.000000 1443.0999999999999091 0.000000 500.000000 1484.5999999999999091 0.000000 1000.000000 1577.0999999999999091 0.000000 2500.000000 1913.4000000000000909 sphere_unit_area_values_test(): sphere_unit_area_values() stores values of the sphere_unit_area function. n sphere_unit_area(n) 1 2.0000000000000000 2 6.2831853071795862 3 12.5663706143591707 4 19.7392088021787195 5 26.3189450695716189 6 31.0062766802998198 7 33.0733617923198082 8 32.4696970113341479 9 29.6865801246483585 10 25.5016403987734499 11 20.7251426732889001 12 16.0231532262550687 13 11.8381738121826796 14 8.3897034104910890 15 5.7216492123495666 16 3.7652900857422908 17 2.3966788175913640 18 1.4786259590003079 19 0.8858104195716824 20 0.5161378278002812 sphere_unit_volume_values_test(): sphere_unit_volume_values() stores values of the sphere_unit_volume function. N sphere_unit_volume(X) 1 2.0000000000000000 2 3.1415926535897931 3 4.1887902047863914 4 4.9348022005446790 5 5.2637890139143249 6 5.1677127800499703 7 4.7247659703314007 8 4.0587121264167676 9 3.2985089027387069 10 2.5501640398773451 11 1.8841038793899001 12 1.3352627688545891 13 0.9106287547832831 14 0.5992645293207921 15 0.3814432808233045 16 0.2353306303588932 17 0.1409811069171390 18 0.0821458866111282 19 0.0466216010300885 20 0.0258068913900141 spherical_harmonic_values_test(): spherical_harmonic_values() stores values of the spherical_harmonic function. L M THETA PHI YR YI 0 0 0.523599 1.047198 0.2820947917738781 0.0000000000000000 1 0 0.523599 1.047198 0.4231421876608172 0.0000000000000000 2 1 0.523599 1.047198 -0.1672616358893223 -0.2897056515173922 3 2 0.523599 1.047198 -0.1106331731112457 0.1916222768312404 4 3 0.523599 1.047198 0.1354974113737760 0.0000000000000000 5 5 0.261799 0.628319 0.0005390423109044 0.0000000000000000 5 4 0.261799 0.628319 -0.0051466904429519 0.0037392894852833 5 3 0.261799 0.628319 0.0137100436134949 -0.0421951755232080 5 2 0.261799 0.628319 0.0609635202226554 0.1876264225575173 5 1 0.261799 0.628319 -0.4170400640977983 -0.3029973424491321 4 2 0.628319 0.785398 0.0000000000000000 0.4139385503112256 4 2 1.884956 0.785398 0.0000000000000000 -0.1003229830187463 4 2 3.141593 0.785398 0.0000000000000000 0.0000000000000000 4 2 4.398230 0.785398 0.0000000000000000 -0.1003229830187463 4 2 5.654867 0.785398 0.0000000000000000 0.4139385503112256 3 -1 0.392699 0.448799 0.3641205966137958 -0.1753512375142586 3 -1 0.392699 0.897598 0.2519792711195075 -0.3159720118970196 3 -1 0.392699 1.346397 0.0899303606570430 -0.3940106541811563 3 -1 0.392699 1.795196 -0.0899303606570430 -0.3940106541811563 3 -1 0.392699 2.243995 -0.2519792711195075 -0.3159720118970196 sqrt_values_test(): sqrt_values() stores values of the SQRT function. X SQRT(X) 0.000000 0.0000000000000000 0.000000 0.0000900000004095 0.090000 0.3000000000000000 0.100000 0.3162277660168379 0.400000 0.6324555320336759 1.000000 1.0000000000000000 2.000000 1.4142135623730949 3.000000 1.7320508075688770 3.141593 1.7724538509055161 19.000000 4.3588989435406740 29.000000 5.3851648071345037 71.000000 8.4261497731763590 97.000000 9.8488578017961057 123456789.000000 11111.1110605555604707 stirling1_values_test(): stirling1_values() stores values of the STIRLING1 function. N M STIRLING1(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() stores values of the STIRLING2 function. N M STIRLING2(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() stores values of the STROMGEN function. X STROMGEN(X) 0.001953 0.0000000000000002 0.007812 0.0000000000002248 0.031250 0.0000000002324502 0.125000 0.0000002471956148 0.500000 0.0002899261098983 1.000000 0.0106981463908097 1.500000 0.0897076509644247 2.000000 0.4004960571959289 3.000000 3.0504104398079095 4.000000 11.3677048584394260 4.125000 12.9606794053247878 4.500000 18.5487139447485063 5.000000 27.8662738219031212 6.000000 51.9633340716993217 8.000000 108.6101674789122882 10.000000 153.7890331655662237 15.000000 193.0266553255872282 20.000000 196.3685016600654194 30.000000 196.5194676600821424 50.000000 196.5195692086831514 struve_h0_values_test(): struve_h0_values() stores values of the struve_h0 function. X struve_h0(X) 0.001953 0.0012433974658847 -0.007812 -0.0049735582423748 0.062500 0.0397714690545369 -0.250000 -0.1580524600165331 1.000000 0.5686566270482879 1.250000 0.6659839931489991 2.000000 0.7908588495080959 -4.000000 -0.1350145734224864 7.500000 0.2008647966816450 11.000000 -0.1114209780026199 11.500000 -0.1702680486598989 -16.000000 -0.1354493180818647 20.000000 0.0943936980813234 25.000000 -0.1018248201600151 -30.000000 0.0960984215541621 50.000000 -0.0853376748261190 75.000000 -0.0768822906370527 -80.000000 0.0476638335914183 100.000000 -0.0708787516896473 -125.000000 0.0657529080733528 struve_h1_values_test(): struve_h1_values() stores values of the struve_h1 function. X struve_h1(X) 0.001953 0.0000008095036958 -0.007812 0.0000129520097241 0.062500 0.0008287161516541 -0.250000 0.0132077483758496 1.000000 0.1984573362019444 1.250000 0.2985382323180470 2.000000 0.6467637282835621 -4.000000 1.0697266613089194 7.500000 0.3883130800042056 11.000000 0.7485424374510771 11.500000 0.8466485464256736 -16.000000 0.5838573246424439 20.000000 0.8060058452421577 25.000000 0.5388036213269295 -30.000000 0.7217503783469900 50.000000 0.5800784479454419 75.000000 0.6015191038544081 -80.000000 0.7061151114728683 100.000000 0.6163111032720134 -125.000000 0.6277848076544366 struve_l0_values_test(): struve_l0_values() stores values of the struve_l0 function. X struve_l0(X) 0.00195312 0.001243398519926282 -0.03125 -0.01989652664788294 0.125 0.07971571325311501 -0.5 -0.3272406993941808 1 0.7102431859378909 2 1.937433757991446 -4 -11.13105020324858 7 168.5006203470327 -10 -2815.652249374595 16 893446.187969784 16.25 1138202.500285145 -17 -2354970.185586019 20 43558282.52764104 22.5 499935164.7603796 -25 -5774560606.440804 30 781672297823.9563 -40 -1.48947747934199e+16 50 2.932553783849336e+20 60 5.894077055609801e+24 -70 -1.201588957912546e+29 struve_l1_values_test(): struve_l1_values() stores values of the struve_l1 function. X struve_l1(X) 0.00195312 8.095041074986513e-07 -0.0078125 0.0002072464909257151 0.0625 0.003319183406689452 -0.25 0.05394218262352266 1 0.2267643810558087 1.25 1.102759787367716 2 9.169277811738684 -4 155.4165665242666 7.5 2670.358285208483 11 865058.8017530463 11.5 1102604.661309494 -16 2284620.949415394 20 42454972.75011198 25 488696145.8799769 -30 5657865129.243105 50 768532038938.321 75 1.470739616325935e+16 -80 2.903078590103557e+20 100 5.844751588390468e+24 -125 1.192975078889231e+29 student_cdf_values_test(): student_cdf_values() stores values of the student_cdf function. C X student_cdf(C,X) 1 0.325 0.6000231200328521 2 0.289 0.600108027913439 3 0.277 0.600115093464893 4 0.271 0.6000995134721354 5 0.267 0.599934198983483 2 0.816 0.7498859393137811 5 0.727 0.7500879487671045 2 2.92 0.9500004222186464 5 2.015 0.9499969138365968 2 6.965 0.9900012348724744 3 4.541 0.9900017619355059 4 3.747 0.9900004567580596 5 3.365 0.9900007637471291 student_noncentral_cdf_values_test(): student_noncentral_cdf_values() stores values of the student_noncentral_cdf function. DF LAM X CDF(DF,LAM,X) 1 0 3 0.8975836176504333 2 0 3 0.9522670169 3 0 3 0.9711655571887813 1 0.5 3 0.8231218863999999 2 0.5 3 0.904902151 3 0.5 3 0.9363471834 1 1 3 0.7301025986 2 1 3 0.8335594263 3 1 3 0.8774010255 1 2 3 0.5248571617 2 2 3 0.6293856597 3 2 3 0.6800271741 1 4 3 0.20590131975 2 4 3 0.2112148916 3 4 3 0.2074730718 15 7 15 0.9981130072 20 7 15 0.999487385 25 7 15 0.9998391562 1 1 0.05 0.168610566972 2 1 0.05 0.16967950985 3 1 0.05 0.1701041003 10 2 4 0.9247683363 10 3 4 0.7483139269 10 4 4 0.4659802096 10 2 5 0.9761872541 10 3 5 0.8979689357 10 4 5 0.7181904627 10 2 6 0.9923658945 10 3 6 0.9610341649 10 4 6 0.868800735 subfactorial_values_test(): subfactorial_values() stores values of the SUBFACTORIAL function. N Subfactorial(N) 0 1 1 0 2 1 3 2 4 9 5 44 6 265 7 1854 8 14833 9 133496 10 1334961 11 14684570 12 176214841 surten_values_test(): surten_values() stores values of the SURTEN function. TC SIGMA(TC) 10 74.22 20 72.73999999999999 30 71.2 40 69.59999999999999 50 67.95 100 58.92 150 48.75 200 37.68 250 26.05 300 14.37 325 8.779999999999999 350 3.67 370 0.4 373.976 0 synch1_values_test(): synch1_values() stores values of the synch1 function. X synch1(X) 0.00195312 0.265148645474874 0.03125 0.6205012997907905 0.125 0.8511257213236801 0.5 0.8708191468754688 1 0.6514228153553639 1.5 0.4506404092032236 2 0.3016359028507394 2.5 0.1981449080444131 3 0.1285657100090638 4 0.05282739669786682 4.25 0.04213929847172031 5 0.02124812977498199 5.5 0.01340025890750554 6 0.008426079731410871 8 0.001288451618675467 10 0.000192238264300869 12 2.822107083400769e-05 15 1.554875797303819e-06 20 1.196863445609745e-08 25 8.956424677223712e-11 synch2_values_test(): synch2_values() stores values of the synch2 function. X synch2(X) 0.00195312 0.1343072727566738 0.03125 0.3348526527242418 0.125 0.5040422411091108 0.5 0.6029652323601679 1 0.4944750621042083 1.5 0.3603606786047336 2 0.2496778549762566 2.5 0.1681383054290583 3 0.1111712234855655 4 0.04692320582610133 4.25 0.03762454586198 5 0.01922212317248411 5.5 0.0122095353436547 6 0.007724964426852578 8 0.001202904421367927 10 0.000181611875695302 12 2.688433800662935e-05 15 1.494221273134583e-06 20 1.160769685438516e-08 25 8.736234374622152e-11 tan_values_test(): tan_values() stores values of the TAN function. X TAN(X) 0 0 0.261799 0.2679491924311227 0.5 0.5463024898437905 0.523599 0.5773502691896257 0.785398 1 1 1.557407724654902 1.0472 1.732050807568877 1.309 3.732050807568877 1.4399 7.59575411272515 1.50535 15.25705168826554 2 -2.185039863261519 3 -0.1425465430742778 3.14159 0 4 1.157821282349577 5 -3.380515006246586 tanh_values_test(): tanh_values() stores values of the TANH function. X TANH(X) -5 -0.9999092042625951 -1 -0.7615941559557649 0 0 0.1 0.09966799462495582 0.2 0.197375320224904 0.3 0.2913126124515909 0.4 0.3799489622552249 0.5 0.4621171572600097 0.6 0.5370495669980353 0.7 0.6043677771171635 0.8 0.664036770267849 0.9 0.7162978701990245 1 0.7615941559557649 2 0.9640275800758169 3 0.9950547536867305 4 0.999329299739067 5 0.9999092042625951 10 0.9999999958776927 tau_values_test(): tau_values() stores values of the TAU function. N TAU(N) 1 1 2 2 3 2 4 3 5 2 6 4 7 2 8 4 9 3 10 4 23 2 72 12 126 12 226 4 300 18 480 24 521 2 610 8 832 14 960 28 thercon_values_test(): thercon_values() stores values of the thermal conductivity function. TC P LAM(TC,P) 0 1 561 0 5 561.3 0 10 561.5 0 25 562.4 0 50 563.7 0 75 565.1 0 100 566.5 0 125 567.9 0 150 569.3 0 175 570.6 0 200 572 0 225 573.4 0 250 574.8 0 275 576.1 0 300 577.5 0 350 580.2 0 400 582.9 0 450 585.5 0 500 588.1 0 550 590.7 0 600 593.3 0 650 595.8 0 700 598.3 0 800 603.1 0 900 607.8 0 1000 612.2 25 1 607.2 50 1 643.6 75 1 666.8 100 1 25.08 150 1 28.85 200 1 33.28 400 1 54.76 600 1 79.89 800 1 107.3 three_j_values_test(): three_j_values() stores values of the three_j function. J1 J2 J3 M1 M2 M3 three_j(X) 1.0 4.5 3.5 1.0 -3.5 2.5 0.2788866755113585 2.0 4.5 3.5 1.0 -3.5 2.5 -0.0953462589245592 3.0 4.5 3.5 1.0 -3.5 2.5 -0.0674199862463242 4.0 4.5 3.5 1.0 -3.5 2.5 0.1533110351679666 5.0 4.5 3.5 1.0 -3.5 2.5 -0.1564465546936860 6.0 4.5 3.5 1.0 -3.5 2.5 0.1099450412156551 7.0 4.5 3.5 1.0 -3.5 2.5 -0.0553623569313172 8.0 4.5 3.5 1.0 -3.5 2.5 0.0179983545113779 tran02_values_test(): tran02_values() stores values of the tran02 function. X tran02(X) 0.00195312 0.001953124793039451 0.03125 0.03124915231433111 0.125 0.1249457719478345 0.5 0.496553636156406 1 0.9730325613551701 1.5 1.412197869593253 2 1.801718567440578 2.5 2.135038533927704 3 2.411050049016954 4 2.806666404563118 4.25 2.877742186329623 5 3.039170604343855 5.5 3.112507492866736 6 3.165668781773858 8 3.262352036781601 10 3.284329114497952 15 3.289789516777579 20 3.28986722266655 30 3.289868133606432 50 3.289868133696453 tran03_values_test(): tran03_values() stores values of the tran03 function. X tran03(X) 0.00195312 1.907348329647638e-06 0.03125 0.0004882613824318079 0.125 0.00780741638484312 0.5 0.1237086871881203 1 0.4798410065724175 1.5 1.026943162203976 2 1.706354721945866 2.5 2.453921744447594 3 3.210604662942247 4 4.579217437229157 4.25 4.872202283294037 5 5.614386613842274 5.5 5.998445586457547 6 6.303395367348096 8 6.957990868836117 10 7.150322712008593 15 7.211073147587188 20 7.212322196638846 30 7.212341416160947 50 7.212341418957566 tran04_values_test(): tran04_values() stores values of the tran04 function. X tran04(X) 0.00195312 2.483526391946183e-09 0.03125 1.017202935361672e-05 0.125 0.0006505333240594077 0.5 0.04115044800415573 1 0.3172440452344265 1.5 1.007944290114237 2 2.201088102433341 2.5 3.884650861915655 3 5.964822397371477 4 10.73193239299862 4.25 11.94002887681937 5 15.35978431688218 5.5 17.37258763309374 6 19.12297601605317 8 23.58397915692194 10 25.27366767703044 15 25.95519821457226 20 25.97535093521224 30 25.97575752208409 50 25.97575760906732 tran05_values_test(): tran05_values() stores values of the tran05 function. X tran05(X) 0.00195312 3.637978036103612e-12 0.03125 2.384056445394844e-07 0.125 6.098220537222697e-05 0.5 0.01541000458637665 1 0.2366158792390948 1.5 1.119875685130763 2 3.229290166368405 2.5 7.036297310516066 3 12.77055769104416 4 29.48833901524585 4.25 34.47134054036226 5 50.26309221817519 5.5 60.81990910112717 6 70.87333442921346 8 101.4778124297779 10 116.3807454024207 15 124.0962390126297 20 124.4227015563255 30 124.4313279083859 50 124.4313306172043 tran06_values_test(): tran06_values() stores values of the tran06 function. X tran06(X) 0.00195312 5.684340595364121e-15 0.03125 5.96011801652474e-09 0.125 6.097842439758057e-06 0.5 0.00615789098663195 1 0.1885436027568084 1.5 1.331925134792166 2 5.085720227169761 2.5 13.72922236546656 3 29.57959248164144 4 88.60083570689986 4.25 109.1603711337301 5 182.2432374957536 5.5 237.6538312558676 6 295.4324674595938 8 506.8124438128045 10 638.7823113494612 15 726.9920355699487 20 732.3033164314685 30 732.4869201588209 50 732.4870046287999 tran07_values_test(): tran07_values() stores values of the tran07 function. X tran07(X) 0.00195312 9.25185633272834e-18 0.03125 1.552109555694987e-10 0.125 6.351623837384172e-07 0.5 0.002563880124662614 1 0.1566532899381165 1.5 1.65382250391811 2 8.376308570950821 2.5 28.07857071783076 3 72.00967604675199 4 281.7490570169191 4.25 366.6022797532779 5 705.560679826036 5.5 996.6192756275562 6 1328.89144304174 8 2798.764027316913 10 3972.13764094165 15 4991.34928393199 20 5078.156263982502 30 5082.077720202871 50 5082.080358004717 tran08_values_test(): tran08_values() stores values of the tran08 function. X tran08(X) 0.00195312 1.548859863453936e-20 0.03125 4.157426911784595e-12 0.125 6.805065124522742e-08 0.5 0.001098170351956301 1 0.1339643277618788 1.5 2.115338780699862 2 14.22787702875074 2.5 59.31206143164784 3 181.3961457704315 4 931.4800192899222 4.25 1281.792811260461 5 2857.283838632924 5.5 4387.297168787773 6 6299.322913940666 8 16589.42627715489 10 27064.7807987974 15 38974.55606254366 20 40400.24071690503 30 40484.31650412065 50 40484.39900189218 tran09_values_test(): tran09_values() stores values of the tran09 function. X tran09(X) 0.00195312 2.64697728700849e-23 0.03125 1.136794365359425e-13 0.125 7.44282462553298e-09 0.5 0.0004802272848541537 1 0.1170024301435868 1.5 2.764897391089991 2 24.71663140582919 2.5 128.2711982884983 3 468.4289480066221 4 3167.39673716279 4.25 4614.08865466302 5 11952.7185453923 5.5 20001.61266647703 6 31011.07327185137 8 103529.4990554113 10 197431.7301714059 15 338260.3041465846 20 361796.0703675076 30 363606.2212477756 50 363608.8055882716 trigamma_values_test(): trigamma_values() stores values of the trigamma function. X trigamma(X) 1.000000 1.6449340668482260 1.100000 1.4332991507927590 1.200000 1.2673772054237791 1.300000 1.1342534349966189 1.400000 1.0253565905295969 1.500000 0.9348022005446793 1.600000 0.8584318931245799 1.700000 0.7932328301639984 1.800000 0.7369741375017002 1.900000 0.6879720582426356 2.000000 0.6449340668482264 truncated_normal_ab_cdf_values_test(): truncated_normal_ab_cdf_values() stores values of the truncated_normal_ab_cdf function. MU SIGMA A B X F 100 25 50 150 90 0.3371694242213513 100 25 50 150 92 0.3685009225506048 100 25 50 150 94 0.4006444233448185 100 25 50 150 96 0.433410706690304 100 25 50 150 98 0.4665988676496338 100 25 50 150 100 0.5 100 25 50 150 102 0.5334011323503662 100 25 50 150 104 0.566589293309696 100 25 50 150 106 0.5993555766551815 100 25 50 150 108 0.6314990774493952 100 25 50 150 110 0.6628305757786487 truncated_normal_ab_pdf_values_test(): truncated_normal_ab_pdf_values() stores values of the truncated_normal_ab_pdf function. MU SIGMA A B X F 100 25 50 150 90 0.01543301171801836 100 25 50 150 92 0.01588394472270638 100 25 50 150 94 0.01624375997031919 100 25 50 150 96 0.01650575046469259 100 25 50 150 98 0.01666496869385951 100 25 50 150 100 0.01671838200940538 100 25 50 150 102 0.01666496869385951 100 25 50 150 104 0.01650575046469259 100 25 50 150 106 0.01624375997031919 100 25 50 150 108 0.01588394472270638 100 25 50 150 110 0.01543301171801836 truncated_normal_a_cdf_values_test(): truncated_normal_a_cdf_values() stores values of the truncated_normal_a_cdf function. MU SIGMA A X F 100 25 50 90 0.3293202045481688 100 25 50 92 0.3599223134505957 100 25 50 94 0.3913175216041539 100 25 50 96 0.4233210140873113 100 25 50 98 0.4557365629792204 100 25 50 100 0.4883601253415709 100 25 50 102 0.5209836877039214 100 25 50 104 0.5533992365958303 100 25 50 106 0.5854027290789878 100 25 50 108 0.6167979372325459 100 25 50 110 0.6474000461349729 truncated_normal_a_pdf_values_test(): truncated_normal_a_pdf_values() stores values of the truncated_normal_a_pdf function. MU SIGMA A X F 100 25 50 90 0.01507373507401876 100 25 50 92 0.01551417047139894 100 25 50 94 0.01586560931024694 100 25 50 96 0.01612150073158793 100 25 50 98 0.01627701240029317 100 25 50 100 0.01632918226724295 100 25 50 102 0.01627701240029317 100 25 50 104 0.01612150073158793 100 25 50 106 0.01586560931024694 100 25 50 108 0.01551417047139894 100 25 50 110 0.01507373507401876 truncated_normal_b_cdf_values_test(): truncated_normal_b_cdf_values() stores values of the truncated_normal_b_cdf function. MU SIGMA B X F 100 25 150 90 0.3525999538650271 100 25 150 92 0.383202062767454 100 25 150 94 0.4145972709210122 100 25 150 96 0.4466007634041696 100 25 150 98 0.4790163122960786 100 25 150 100 0.5116398746584291 100 25 150 102 0.5442634370207796 100 25 150 104 0.5766789859126887 100 25 150 106 0.6086824783958461 100 25 150 108 0.6400776865494043 100 25 150 110 0.6706797954518312 truncated_normal_b_pdf_values_test(): truncated_normal_b_pdf_values() stores values of the truncated_normal_b_pdf function. MU SIGMA B X F 100 25 150 90 0.01507373507401876 100 25 150 92 0.01551417047139894 100 25 150 94 0.01586560931024694 100 25 150 96 0.01612150073158793 100 25 150 98 0.01627701240029317 100 25 150 100 0.01632918226724295 100 25 150 102 0.01627701240029317 100 25 150 104 0.01612150073158793 100 25 150 106 0.01586560931024694 100 25 150 108 0.01551417047139894 100 25 150 110 0.01507373507401876 tsat_values_test(): tsat_values() stores values of the TSAT function. P TSAT(P) 0.0061173 0.01 0.012 9.654999999999999 0.025 21.08 0.055 34.589 0.08 41.518 0.11 47.695 0.16 55.327 0.25 64.98 0.5 81.339 0.75 91.783 1 99.63200000000001 1.5 111.378 2 120.443 5 151.866 10 179.916 20 212.417 50 263.977 100 311.031 200 365.8 220.55 373.976 van_der_corput_values_test(): van_der_corput_values() stores values of the van_der_corput function. BASE SEED VALUE 2 0 0 2 1 0.5 2 2 0.25 2 3 0.75 2 4 0.125 2 5 0.625 2 6 0.375 2 7 0.875 2 8 0.0625 3 0 0 3 1 0.333333333333 3 2 0.666666666667 3 3 0.111111111111 3 4 0.444444444444 3 5 0.777777777778 3 6 0.222222222222 3 7 0.555555555556 3 8 0.888888888889 4 0 0 4 1 0.25 4 2 0.5 4 3 0.75 4 4 0.0625 4 5 0.3125 4 6 0.5625 4 7 0.8125 4 8 0.125 2 10 0.3125 3 10 0.37037037037 4 10 0.625 5 10 0.08 7 10 0.448979591837 11 10 0.909090909091 13 10 0.769230769231 2 100 0.1484375 3 100 0.411522633745 4 100 0.09765625 5 100 0.032 7 100 0.291545189504 11 100 0.165289256198 13 100 0.733727810651 2 1000 0.0927734375 3 1000 0.347508001829 4 1000 0.1708984375 5 1000 0.00512 7 1000 0.916284881299 11 1000 0.931630353118 13 1000 0.990441511152 2 10000 0.0347290039062 3 10000 0.386120002032 4 10000 0.0189208984375 5 10000 0.000512 7 10000 0.574998512525 11 10000 0.152995014002 13 10000 0.245929764364 29 1000 0.488744925991 29 1001 0.523227684612 29 1002 0.557710443233 29 1003 0.592193201853 29 1004 0.626675960474 71 1000 0.0872842689942 71 1001 0.101368776037 71 1002 0.115453283079 71 1003 0.129537790121 71 1004 0.143622297163 173 1000 0.780513882856 173 1001 0.786294229677 173 1002 0.792074576498 173 1003 0.797854923319 173 1004 0.803635270139 409 1000 0.444999730992 409 1001 0.447444718767 409 1002 0.449889706542 409 1003 0.452334694317 409 1004 0.454779682092 viscosity_values_test(): viscosity_values() stores values of the VISCOSITY function. TC P ETA(TC,P) 0 1 1792 0 5 1791 0 10 1790 0 25 1786 0 50 1780 0 75 1775 0 100 1769 0 125 1764 0 150 1759 0 175 1754 0 200 1749 0 225 1744 0 250 1739 0 275 1735 0 300 1731 0 350 1722 0 400 1714 0 450 1707 0 500 1700 0 550 1694 0 600 1687 0 650 1682 0 700 1676 0 800 1667 0 900 1659 0 1000 1653 25 1 890.8 50 1 547.1 75 1 378.4 100 1 12.28 200 1 16.18 400 1 24.45 600 1 32.61 800 1 40.38 von_mises_cdf_values_test(): von_mises_cdf_values() stores values of the von Mises CDF. A B X CDF(A,B,X) 0 1 -2.61799 0.0253508995628118 0 1 -1.5708 0.1097539041177346 0 1 0 0.5 0 1 1.0472 0.8043381312498558 0 1 2.0944 0.9417460124555197 1 2 1 0.5 1 2 1.2 0.6018204118446155 1 2 1.4 0.695935693312223 1 2 1.6 0.7765935901304593 1 2 1.8 0.8410725934916615 1 2 2 0.8895777369550366 -2 3 0 0.9960322705517926 -1 3 0 0.9404336090170247 0 3 0 0.5 1 3 0 0.0595663909829753 2 3 0 0.003967729448207649 3 3 0 0.000232195395811193 0 0 0.785398 0.625 0 1 0.785398 0.7438406999109122 0 2 0.785398 0.8369224904294019 0 3 0.785398 0.8941711407897124 0 4 0.785398 0.9291058600568743 0 5 0.785398 0.9514289900655436 weekday_values_test(): weekday_values stores() values of the weekday for a given Y/M/D date Y M D W -587 7 30 1 -169 12 8 4 70 9 26 4 135 10 3 1 470 1 7 4 576 5 18 2 694 11 7 7 1013 4 19 1 1066 10 14 7 1096 5 18 1 1190 3 16 6 1240 3 3 7 1288 3 26 6 1298 4 20 1 1391 6 4 1 1436 1 25 4 1492 3 31 7 1553 9 9 7 1560 2 24 7 1648 6 10 4 1680 6 30 1 1716 7 24 6 1768 6 19 1 1819 8 2 2 1839 3 27 4 1903 4 19 1 1929 8 25 1 1941 9 29 2 1943 4 19 2 1943 10 7 5 1992 3 17 3 1996 2 25 1 2038 11 10 4 2094 7 18 1 weibull_cdf_values_test(): weibull_cdf_values() stores values of the von Mises CDF. ALPHA BETA X CDF(ALPHA,BETA,X) 1 0.5 1 0.8646647167633873 1 0.5 2 0.9816843611112658 1 0.5 3 0.9975212478233336 1 0.5 4 0.9996645373720975 1 2 2 0.6321205588285577 1 3 2 0.486582880967408 1 4 2 0.3934693402873666 1 5 2 0.3296799539643607 2 2 3 0.8946007754381357 3 2 3 0.965781881688334 4 2 3 0.9936702845725143 5 2 3 0.999496410950263 wright_omega_values_test(): wright_omega_values() stores values of the Wright Omega function. Z.real Z.imag FZ.real FZ.imag 0 0 0.5671432904097838 0 1 0 1 0 3.71828 0 2.718281828459045 0 -1 3.14159 -1 0 -1 -3.14159 -1 0 -1.30685 3.14159 -2 0 -1.30685 -3.14159 -0.40637573995996 0 0 2.5708 0 1 0 3.14159 -0.3181315052047641 1.337235701430689 1 1 0.9372082083733697 0.5054213160131512 zeta_values_test(): zeta_values() stores values of the ZETA function. N ZETA(N) 2 1.6449340668482264 3 1.2020569031595942 4 1.0823232337111381 5 1.0369277551433700 6 1.0173430619844492 7 1.0083492773819229 8 1.0040773561979444 9 1.0020083929260821 10 1.0009945751278180 11 1.0004941886041194 12 1.0002460865533080 16 1.0000152822594086 20 1.0000009539620338 30 1.0000000009313275 40 1.0000000000009095 zeta_m1_values_test(): zeta_m1_values() stores values of the zeta_MINUS_ONE function. N zeta_m1(N) 2.000000 6.4493406684822641e-01 2.500000 3.4148725730000001e-01 3.000000 2.0205690315959429e-01 3.500000 1.2673386730000000e-01 4.000000 8.2323233711138186e-02 5.000000 3.6927755143369927e-02 6.000000 1.7343061984449140e-02 7.000000 8.3492773819228271e-03 8.000000 4.0773561979443396e-03 9.000000 2.0083929260822143e-03 10.000000 9.9457512781808526e-04 11.000000 4.9418860411946453e-04 12.000000 2.4608655330804832e-04 16.000000 1.5282259408651871e-05 20.000000 9.5396203387280002e-07 30.000000 9.3132743242000005e-11 40.000000 9.0949477999999997e-13 test_values_test(): Normal end of execution. Tue Mar 19 11:19:33 2024