11 March 2008 11:50:17 AM TEST_VALUES_PRB: C++ version, Test the routines in the TEST_VALUES library. TEST001: ABRAM0_VALUES stores values of the Abramowitz function of order 0. X ABRAM0(X) 0.001953125 0.8737772630698536 0.0078125 0.8472185965045692 0.03125 0.772889344839883 0.125 0.5968434585345015 0.5 0.2987173528367589 1 0.1500459645051639 1.25 0.1111466241915796 1.5 0.0839095671531519 1.875 0.05655232171794342 2 0.04987649660303379 2.125 0.04410088921976279 3 0.01973853518025406 4 0.008619308828716149 5 0.004022478816254013 6 0.001971865845816489 7 0.001004586834013354 10 0.000157269172633045 15 1.035266691235026e-05 20 9.122975919095675e-07 40 2.56282877379527e-10 TEST002: ABRAM1_VALUES stores values of the Abramowitz function of order 1. X ABRAM1(X) 0.001953125 0.4982821984879992 0.0078125 0.4932439177304729 0.03125 0.4743161278469123 0.125 0.4109598325876041 0.5 0.2531761738822704 1 0.1465633813859778 1.25 0.1142154705601837 1.5 0.09002630738348376 1.875 0.0640882141707423 2 0.05744661431416619 2.125 0.05158162456480073 3 0.02526371955577641 4 0.01193080333019659 5 0.005927054228091528 6 0.003060921535801783 7 0.001630738213697955 10 0.0002837185191695945 15 2.112215012132324e-05 20 2.034457889260163e-06 40 7.111651723620965e-10 TEST003: ABRAM2_VALUES stores values of the Abramowitz function of order 2. X ABRAM3(X) 0.001953125 0.4421385816210791 0.0078125 0.4392337954568403 0.03125 0.427898572970926 0.125 0.3865282566185451 0.5 0.2653820441323137 1 0.1684873483833459 1.25 0.1360920003251323 1.5 0.1107033002772792 1.875 0.08212601999553039 2 0.07453878199959459 2.125 0.06773203437761281 3 0.03564180869881185 4 0.01795658995661827 5 0.009405873714357537 6 0.005080935620429921 7 0.002814956541420972 10 0.000538086964225593 15 4.482175638014632e-05 20 4.68906784273241e-06 40 2.016154485099642e-09 TEST0035: AGM_VALUES stores values of the arithmetic geometric mean function. A B AGM(A,B) 22 96 52.27464119870424 83 56 68.83653005985852 42 7 20.65930119673401 26 11 17.69685487374365 4 63 23.8670497217533 6 45 20.71701598280599 40 75 56.12784225561668 80 0 0 90 35 59.26956508122964 9 1 3.936235503649555 53 53 53 1 2 1.456791031046907 1 4 2.243028580287603 1 8 3.615756177597363 1.5 8 4.081692408022163 TEST004: AIRY_AI_VALUES stores values of the Airy functions Ai(X). X Ai(X) 0 0.3550280538878172 0.1 0.3292031299435381 0.2 0.303703154286382 0.3 0.2788064819550049 0.4 0.2547423542956763 0.5 0.2316936064808335 0.6 0.2098000616663795 0.7 0.1891624003981501 0.8 0.1698463174443649 0.9 0.1518868036405444 1 0.1352924163128814 TEST005: AIRY_AI_INT_VALUES stores values of the integral of the Airy Ai function. X FX -12 -0.7522883891661012 -11 -0.5734835018585489 -10 -0.7656984031342129 -9.5 -0.6518101550538247 -9 -0.5588197489447188 -6.5 -0.5690235287071681 -4 -0.4780074964292617 -1 -0.4656739834670686 -0.25 -0.09678314094561802 -0.0009765625 -0.0003468304985703561 0.0009765625 0.0003465836691792793 0.0078125 0.002765758184605123 0.5 0.1459533049118572 1 0.2363173419171098 4 0.3328926453861221 4.5 0.3331875912977942 6 0.3333294517052385 8 0.3333333172424836 10 0.333333333299169 12 0.3333333333332938 TEST006: AIRY_AI_PRIME_VALUES stores values of the derivative of the Airy function Ai'(X). X Ai' 0 -0.2588194037928068 0.1 -0.2571304219075862 0.2 -0.2524054702856195 0.3 -0.2451463642190548 0.4 -0.2358320344192082 0.5 -0.2249105326646839 0.6 -0.2127932593891585 0.7 -0.1998511915822805 0.8 -0.1864128638072717 0.9 -0.1727638434616347 1 -0.1591474412967932 TEST007: AIRY_BI_VALUES stores values of the Airy function Bi. X Bi 0 0.6149266274460007 0.1 0.6598616901941892 0.2 0.7054642029186612 0.3 0.7524855850873156 0.4 0.8017730000135972 0.5 0.8542770431031556 0.6 0.9110633416949405 0.7 0.9733286558781659 0.8 1.042422171231561 0.9 1.119872813134447 1 1.207423594952871 TEST008: AIRY_BI_INT_VALUES stores values of the integral of the Airy Bi function. X FX -12 0.01766081903155463 -10 -0.01504042480614002 -8 0.01475644629322766 -7.5 -0.1184730426484845 -7 -0.06491674126616585 -6.5 0.09726083246438104 -4 0.05076005849528754 -1 -0.3730050096342949 -0.25 -0.1396298844266658 -0.001953125 -0.00120017352667233 0.001953125 0.001201883611789035 0.5 0.3653384655095201 1 0.8727691167380082 4 48.21947526380343 8 440065.2580490418 8.5 1760815.39762283 9 7377921.170522001 10 147809803.1074067 12 97037614223.61343 14 116327376388098.8 TEST009: AIRY_BI_PRIME_VALUES stores values of the derivative of Airy function Bi'(X). X Bi' 0 0.4482883573538264 0.1 0.4515126311496465 0.2 0.4617892843621509 0.3 0.480049028752448 0.4 0.5072816760506224 0.5 0.5445725641405923 0.6 0.5931444786342857 0.7 0.65440591917214 0.8 0.7300069016152518 0.9 0.821903890307209 1 0.9324359333927756 TEST0093: AIRY_CAI_VALUES stores values of the Airy functions Ai(X) for complex argument. X Ai 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 TEST0095: AIRY_CBI_VALUES stores values of the Airy functions Bi(X) for complex argument. X Bi 1 0 1.207423594952871 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 0 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 TEST010: AIRY_GI_VALUES stores values of the modified Airy function Gi(X). X Gi -0.001953125 0.2046830807004054 -0.125 0.183746628325579 -1 -0.1166722172960153 -4 0.3146693490272956 -8 -0.3708904072242626 -8.25 -0.2529305977242402 -9 0.289674106586927 -10 -0.3464483649263409 -11 0.2807603591387305 -13 0.2181499450809486 0.001953125 0.205266790008105 0.125 0.2212369536378477 1 0.2352184398104379 4 0.08283430336376874 7 0.04575738549098928 7.25 0.04415001201460516 8 0.03995113371950891 9 0.03546770683394967 10 0.03189600510067959 12 0.02655689271351241 TEST011: AIRY_HI_VALUES stores values of the modified Airy function Hi(X). X Hi -0.001953125 0.4093679827845889 -0.125 0.3749529160804887 -1 0.2206696067929599 -4 0.07756535667970371 -8 0.03963882647312472 -8.25 0.03845007257500415 -9 0.0352732168683179 -10 0.03176853528250227 -11 0.02889440828805139 -13 0.02446328401167854 0.001953125 0.4105354013999894 0.125 0.4499350238120499 1 0.9722051551424333 4 83.76423710510437 7 80327.74495204476 7.25 155141.3884774911 8 1199585.964173326 9 21472868.85596764 10 455641153.5163291 12 329807225829.0476 TEST0114: ARCCOS_VALUES stores values of the arc cosine function. X FX -0.1 1.670963747956457 0 1.570796326794897 0.1 1.470628905633337 0.2 1.369438406004566 0.3 1.266103672779499 0.4 1.159279480727408 0.5 1.047197551196598 0.6 0.9272952180016122 0.7 0.7953988301841436 0.8 0.6435011087932844 0.9 0.4510268117962624 1 0 TEST01145: ARCCOSH_VALUES stores values of the hyperbolic arc cosine function. X FX 1 0 1.01 0.1413037694856486 1.1 0.4435682543851152 1.2 0.6223625037147786 1.3 0.7564329108569596 1.4 0.8670147264905651 1.5 0.9624236501192069 2 1.316957896924817 3 1.762747174039086 3.141592653589793 1.811526272460853 4 2.06343706889556 5 2.292431669561178 10 2.993222846126381 100 5.298292365610485 1000 7.600902209541989 TEST0115: ARCSIN_VALUES stores values of the arc sine function. X FX -0.1 -0.1001674211615598 0 0 0.1 0.1001674211615598 0.2 0.2013579207903308 0.3 0.3046926540153975 0.4 0.411516846067488 0.5 0.5235987755982989 0.6 0.6435011087932844 0.7 0.7753974966107531 0.8 0.9272952180016122 0.9 1.119769514998634 1 1.570796326794897 TEST01155: ARCSINH_VALUES stores values of the hyperbolic arc sine function. X FX -5 -2.312438341272752 -1 -0.881373587019543 0 0 0.1 0.09983407889920756 0.2 0.1986901103492414 0.3 0.2956730475634224 0.4 0.3900353197707153 0.5 0.4812118250596035 0.6 0.5688248987322475 0.7 0.6526665660823557 0.8 0.7326682560454109 0.9 0.8088669356527824 1 0.881373587019543 2 1.44363547517881 3 1.818446459232067 4 2.094712547261101 5 2.312438341272752 10 2.99822295029797 100 5.298342365610589 1000 7.600902709541988 TEST0116: ARCTAN_VALUES stores values of the arc tangent function. X FX 0 0 0.25 0.2449786631268641 0.3333333333333333 0.3217505543966422 0.5 0.4636476090008061 1 0.7853981633974483 2 1.10714871779409 3 1.249045772398254 4 1.325817663668033 5 1.373400766945016 10 1.471127674303735 20 1.520837931072954 TEST012: ARCTAN_INT_VALUES stores values of the arctangent integral. X FX 0.001953125 0.001953124172158848 -0.00390625 -0.003906243377298071 0.0078125 0.00781244701925765 0.015625 0.01562457618199653 -0.03125 -0.0312466103494854 0.0625 0.0624729113350144 0.125 0.1247841971738965 -0.25 -0.2483017509823069 0.5 0.4872223582945224 1 0.915965594177219 1.5 1.27496944849438 -2 -1.576015403446323 4 2.425887841285909 8 3.3911633326293 16 4.417645091942219 -20 -4.755671374954725 25 5.096191215093411 30 5.375917573571487 -50 -6.164990478502749 100 7.243784301308353 TEST0123: ARCTANH_VALUES stores values of the hyperbolic arc tangent function. X FX -0.5 -0.5493061443340549 0 0 0.001 0.001000000333333533 0.1 0.1003353477310756 0.2 0.2027325540540822 0.3 0.3095196042031117 0.4 0.4236489301936018 0.5 0.5493061443340549 0.6 0.6931471805599453 0.7 0.8673005276940532 0.8 1.09861228866811 0.9 1.47221948958322 0.99 2.646652412362246 0.999 3.8002011672502 0.999999 7.254328619262047 TEST0127: BEI0_VALUES stores values of the Kelvin function BEI of order 0. X FX 0 0 0.5 0.06249321838219946 1 0.2495660400366597 1.5 0.5575600623030867 2 0.9722916273066612 2.5 1.457182044159804 3 1.937586785266043 3.5 2.283249966853915 4 2.2926903226993 4.5 1.686017203632139 5 0.1160343815502004 TEST0128: BEI1_VALUES stores values of the Kelvin function BEI of order 1. X FX 0 0 0.5 0.1711951797170153 1 0.3075566313755366 1.5 0.3678649890020899 2 0.2997754370020335 2.5 0.03866844396595048 3 -0.4874541770160708 3.5 -1.344042373111174 4 -2.563821688561078 4.5 -4.105685408400878 5 -5.797907901792625 TEST013: 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 TEST0134: BER0_VALUES stores values of the Kelvin function BER of order 0. X FX 0 1 0.5 0.9990234639908383 1 0.9843817812130869 1.5 0.9210721835462558 2 0.7517341827138082 2.5 0.3999684171295313 3 -0.2213802495986939 3.5 -1.193598179589928 4 -2.56341655725858 4.5 -4.299086551599756 5 -6.230082478666358 TEST0135: BER1_VALUES stores values of the Kelvin function BER of order 1. X FX 0 0 0.5 -0.1822431237551121 1 -0.3958682610197114 1.5 -0.6648654179597691 2 -0.9970776519264285 2.5 -1.373096897645111 3 -1.732644221128481 3.5 -1.959644131289749 4 -1.869248459031899 4.5 -1.202821631480086 5 0.3597766667766728 TEST014: BERNOULLI_NUMBER_VALUES returns values of the Bernoulli numbers. N B(N) 0 1 1 -0.5 2 0.1666666666666667 3 0 4 -0.03333333333333333 6 -0.0238095238095238 8 -0.03333333333333333 10 0.07575757575757575 20 -529.1242424242424 30 601580873.9006424 TEST015: BERNOULLI_POLY_VALUES returns values of the Bernoulli Polynomials. N X BERNOULLI(N)(X) 0 0.2 1 1 0.2 -0.3 2 0.2 0.006666666666666667 3 0.2 0.048 4 0.2 -0.007733333333333333 5 0.2 -0.02368 6 0.2 0.00691352380952381 7 0.2 0.0249088 8 0.2 -0.01014997333333333 9 0.2 -0.045278208 10 0.2 0.02332631815757576 5 -0.5 -0.3125 5 -0.4 -0.11424 5 -0.3 -0.01768 5 -0.2 0.01568 5 -0.1 0.01474 5 0 0 5 0.1 -0.01524 5 0.2 -0.02368 5 0.3 -0.02282 5 0.4 -0.01376 5 0.5 0 5 0.6 0.01376 5 0.7 0.02282 5 0.8 0.02368 5 0.9 0.01524 5 1 0 TEST016: BERNSTEIN_POLY_VALUES returns values of the Bernstein Polynomials. N K X BERNSTEIN(N,K)(X) 0 0 0.25 1 1 0 0.25 0.75 1 1 0.25 0.25 2 0 0.25 0.5625 2 1 0.25 0.375 2 2 0.25 0.0625 3 0 0.25 0.421875 3 1 0.25 0.421875 3 2 0.25 0.140625 3 3 0.25 0.015625 4 0 0.25 0.31640625 4 1 0.25 0.421875 4 2 0.25 0.2109375 4 3 0.25 0.046875 4 4 0.25 0.00390625 TEST017: BESSEL_I0_VALUES stores values of the Bessel I0 function. X I0(X) 0 1 0.2 1.010025027795146 0.4 1.040401782229341 0.6 1.09204536431734 0.8 1.166514922869803 1 1.266065877752008 1.2 1.393725584134064 1.4 1.553395099731217 1.6 1.749980639738909 1.8 1.989559356618051 2 2.279585302336067 2.5 3.289839144050123 3 4.880792585865024 3.5 7.37820343222548 4 11.30192195213633 4.5 17.48117185560928 5 27.23987182360445 6 67.23440697647798 8 427.5641157218048 10 2815.716628466254 TEST018: BESSEL_I0_INT_VALUES stores values of the integral of the Bessel I0 function. X FX 0.001953125 0.001953125620881805 -0.00390625 -0.003906254967056573 0.0625 0.06252034803254657 0.125 0.1251628558136697 -0.5 -0.5105148087974031 1 1.08652109702359 2 2.775001905428253 -4 -13.77520886803972 8 464.2437205810611 18 6411186.765802158 -18.5 -10414860.80317586 20 44758598.91385575 -21 -118529853.1155829 22 314300782.2071599 -23 -834402129.0079432 24 2217536757.90743 25 5899173184.280364 -27 -41857073244.69152 30 795538858184.7236 40 1.50897150827192e+16 TEST0185: BESSEL_I0_SPHERICAL_VALUES stores values of the spherical Bessel i0 function. X i0(X) 0.1 1.00166750019844 0.2 1.00668001270547 0.4 1.026880814507039 0.6 1.061089303580402 0.8 1.110132477734529 1 1.175201193643801 1.2 1.257884462843477 1.4 1.360215358179667 1.6 1.484729970750144 1.8 1.634541271164267 2 1.813430203923509 2.2 2.025956895698133 2.4 2.277595505698373 2.6 2.574897010920645 2.8 2.925685126512827 3 3.339291642469967 3.2 3.826838748926716 3.4 4.401577467270101 3.6 5.079293155726485 3.8 5.878791279137455 4 6.822479299281938 TEST019: BESSEL_I1_VALUES stores values of the Bessel I1 function. X I1(X) 0 0 0.2 0.1005008340281251 0.4 0.2040267557335706 0.6 0.3137040256049221 0.8 0.4328648026206398 1 0.565159103992485 1.2 0.7146779415526431 1.4 0.8860919814143274 1.6 1.08481063512988 1.8 1.317167230391899 2 1.590636854637329 2.5 2.516716245288698 3 3.953370217402609 3.5 6.205834922258365 4 9.759465153704451 4.5 15.38922275373592 5 24.33564214245053 6 61.34193677764024 8 399.8731367825601 10 2670.988303701255 TEST0195: BESSEL_I1_SPHERICAL_VALUES stores values of the spherical Bessel i1 function. X i1(X) 0.1 0.03336667857363341 0.2 0.06693371456802955 0.4 0.1354788933285401 0.6 0.2072931911031093 0.8 0.2841280857128948 1 0.3678794411714423 1.2 0.4606425870674146 1.4 0.5647736480096238 1.6 0.6829590627779635 1.8 0.8182955028627777 2 0.9743827435800611 2.2 1.155432469636406 2.4 1.366396525527973 2.6 1.613118767572064 2.8 1.902515460838681 3 2.242790117769266 3.2 2.643689828630357 3.4 3.116811526884873 3.6 3.675968313148932 3.8 4.337627987747642 4 5.121438384183637 TEST020: BESSEL_IN_VALUES stores values of the Bessel In function. X IN(X) 2 0.2 0.005016687513894678 2 1 0.1357476697670383 2 2 0.6889484476987382 2 2.5 1.276466147819164 2 3 2.245212440929951 2 5 17.50561496662424 2 10 2281.518967726004 2 20 39312785.22104076 3 1 0.0221684249243319 3 2 0.2127399592398527 3 5 10.33115016915114 3 10 1758.380716610853 3 50 2.677764138883941e+20 5 1 0.0002714631559569719 5 2 0.009825679323131702 5 5 2.157974547322546 5 10 777.18828640326 5 50 2.278548307911282e+20 10 1 2.752948039836874e-10 10 2 3.016963879350684e-07 10 5 0.004580044419176051 10 10 21.89170616372337 10 50 1.071597159477637e+20 20 1 3.96683598581902e-25 20 2 4.310560576109548e-19 20 5 5.024239357971806e-11 20 10 0.0001250799735644948 20 50 5.442008402752998e+18 TEST0205: BESSEL_IX_VALUES stores values of the Bessel In function for NONINTEGER order. X IN(X) 0.5 0.2 0.3592084175833614 0.5 1 0.9376748882454876 0.5 2 2.046236863089055 0.5 2.5 3.053093538196718 0.5 3 4.614822903407601 0.5 5 26.47754749755907 0.5 10 2778.784603874571 0.5 20 43279746.27242893 1.5 1 0.2935253263474798 1.5 2 1.09947318863311 1.5 5 21.18444226479414 1.5 10 2500.906154942118 1.5 50 2.866653715931464e+20 2.5 1 0.05709890920304825 2.5 2 0.3970270801393905 2.5 5 13.76688213868258 2.5 10 2028.512757391936 2.5 50 2.753157630035402e+20 1.25 1 0.4139416015642352 1.25 2 1.340196758982897 1.25 5 22.8571551036467 1.25 10 2593.006763432002 1.25 50 2.886630075077766e+20 2.75 1 0.03590910483251082 2.75 2 0.2931108636266483 2.75 5 11.99397010023068 2.75 10 1894.575731562383 2.75 50 2.716911375760483e+20 TEST021: BESSEL_J0_VALUES stores values of the Bessel J0 function. X J0(X) -5 -0.1775967713143383 -4 -0.3971498098638474 -3 -0.2600519549019334 -2 0.2238907791412357 -1 0.7651976865579666 0 1 1 0.7651976865579666 2 0.2238907791412357 3 -0.2600519549019334 4 -0.3971498098638474 5 -0.1775967713143383 6 0.1506452572509969 7 0.3000792705195556 8 0.1716508071375539 9 -0.09033361118287613 10 -0.2459357644513483 11 -0.1711903004071961 12 0.04768931079683354 13 0.2069261023770678 14 0.1710734761104587 15 -0.01422447282678077 TEST022: BESSEL_J0_INT_VALUES stores values of the integral of the Bessel J0 function. X FX 0.0009765625 0.0009765624223897882 0.00390625 0.003906245032949111 -0.0625 -0.06247965792791793 0.125 0.1248373349212048 -0.5 -0.4896805066460451 1 0.9197304100897602 -2 -1.425770293197027 4 1.024734159460607 -8 -1.21074683483045 16 1.100865203273619 -16.5 -1.006033482990413 18 0.8133057266248596 -20 -1.058378821421128 25 0.8710149211654588 -30 -0.8842490888254749 40 1.125776150359991 -50 -0.9014121225818346 75 0.9144134436964779 -80 -0.944822819383344 100 0.9226625569601661 TEST023: BESSEL_J0_SPHERICAL_VALUES stores values of the spherical Bessel j0 function. X j0(X) 0.1 0.9983341664682815 0.2 0.9933466539753061 0.4 0.9735458557716262 0.6 0.9410707889917256 0.8 0.8966951136244035 1 0.8414709848078965 1.2 0.7766992383060221 1.4 0.7038926642774715 1.6 0.6247335019009407 1.8 0.5410264615989973 2 0.4546487134128408 2.2 0.367498365372541 2.4 0.2814429918963129 2.6 0.1982697583928709 2.8 0.1196386250556803 3 0.04704000268662241 3.2 -0.01824191982111872 3.4 -0.0751591476549504 3.6 -0.1229223453596812 3.8 -0.1610152344586103 4 -0.1892006238269821 TEST024: BESSEL_J1_VALUES stores values of the Bessel J1 function. X J1(X) -5 0.3275791375914652 -4 0.06604332802354913 -3 -0.3390589585259365 -2 -0.5767248077568734 -1 -0.4400505857449335 0 0 1 0.4400505857449335 2 0.5767248077568734 3 0.3390589585259365 4 -0.06604332802354913 5 -0.3275791375914652 6 -0.2766838581275656 7 -0.004682823482345833 8 0.2346363468539146 9 0.2453117865733253 10 0.04347274616886144 11 -0.1767852989567215 12 -0.2234471044906276 13 -0.07031805212177837 14 0.1333751546987933 15 0.2051040386135228 TEST025: BESSEL_J1_SPHERICAL_VALUES stores values of the spherical Bessel j1 function. X j1(X) 0.1 0.03330001190255757 0.2 0.06640038067032222 0.4 0.1312121544218529 0.6 0.1928919568034122 0.8 0.2499855053465475 1 0.3011686789397568 1.2 0.3452845698577903 1.4 0.3813753724123076 1.6 0.4087081401263934 1.8 0.4267936423844913 2 0.4353977749799916 2.2 0.4345452193763121 2.4 0.4245152947656493 2.6 0.4058301968314685 2.8 0.3792360591872637 3 0.345677499762356 3.2 0.3062665174917607 3.4 0.2622467779189737 3.6 0.2149544641595738 3.8 0.165776967751528 4 0.1161107492591575 TEST026: BESSEL_JN_VALUES stores values of the Bessel Jn function. X JN(X) 2 1 0.1149034849319005 2 2 0.3528340286156377 2 5 0.04656511627775222 2 10 0.2546303136851206 2 50 -0.05971280079425882 5 1 0.0002497577302112344 5 2 0.007039629755871685 5 5 0.2611405461201701 5 10 -0.2340615281867936 5 50 -0.08140024769656964 10 1 2.630615123687453e-10 10 2 2.515386282716737e-07 10 5 0.001467802647310474 10 10 0.2074861066333589 10 50 -0.1138478491494694 20 1 3.873503008524658e-25 20 2 3.918972805090754e-19 20 5 2.770330052128942e-11 20 10 1.15133692478134e-05 20 50 -0.1167043527595797 TEST0265: BESSEL_JX_VALUES stores values of the Bessel Jn function for NONINTEGER order. X JN(X) 0.5 0.2 0.3544507442114011 0.5 1 0.6713967071418031 0.5 2 0.5130161365618278 0.5 2.5 0.3020049060623657 0.5 3 0.06500818287737578 0.5 5 -0.3421679847981618 0.5 10 -0.1372637357550505 0.5 20 0.1628807638550299 1.5 1 0.240297839123427 1.5 2 0.4912937786871623 1.5 5 -0.1696513061447408 1.5 10 0.1979824927558931 1.5 50 -0.109476872988318 2.5 1 0.04949681022847794 2.5 2 0.2239245314689158 2.5 5 0.2403772011113174 2.5 10 0.1966584835818184 2.5 50 0.02303721950962553 1.25 1 0.3314145508558904 1.25 2 0.546173424040284 1.25 5 -0.2616584152094124 1.25 10 0.1296035513791289 1.25 50 -0.1117432171933552 2.75 1 0.03142623570527935 2.75 2 0.1717922192746527 2.75 5 0.3126634069544786 2.75 10 0.1340289119304364 2.75 50 0.06235967135106445 TEST027: BESSEL_K0_VALUES stores values of the Bessel K0 function. X K0(X) 0.1 2.427069024702017 0.2 1.752703855528146 0.4 1.114529134524434 0.6 0.7775220919047293 0.8 0.5653471052658957 1 0.4210244382407083 1.2 0.3185082202865936 1.4 0.2436550611815419 1.6 0.1879547519693323 1.8 0.145931400489828 2 0.1138938727495334 2.5 0.06234755320036619 3 0.03473950438627925 3.5 0.01959889717036849 4 0.01115967608585302 4.5 0.006399857243233975 5 0.003691098334042594 6 0.001243994328013123 8 0.0001464707052228154 10 1.778006231616765e-05 TEST028: BESSEL_K0_INT_VALUES stores values of the integral of the Bessel K0 function. X FX 0.0009765625 0.007858792956346679 0.00390625 0.02601999161733058 0.0625 0.2431184223754117 0.125 0.3999963375048051 0.5 0.9271025209311491 1 1.242509848623778 2 1.473675734316829 4 1.560649570605174 5 1.567387390728366 6 1.569634553269374 6.5 1.570115344325079 8 1.570657485289444 10 1.570779311615979 12 1.570794206646577 15 1.570796231546919 20 1.570796326234015 30 1.570796326794876 50 1.570796326794897 80 1.570796326794897 100 1.570796326794897 TEST029: BESSEL_K1_VALUES stores values of the Bessel K1 function. X K1(X) 0.1 9.853844780870606 0.2 4.775972543220472 0.4 2.184354424732687 0.6 1.302834939763502 0.8 0.8617816344721803 1 0.6019072301972346 1.2 0.434592391060715 1.4 0.3208359022298758 1.6 0.2406339113576119 1.8 0.182623099801747 2 0.1398658818165224 2.5 0.07389081634774707 3 0.04015643112819418 3.5 0.02223939292592383 4 0.01248349888726843 4.5 0.00707809490896809 5 0.004044613445452164 6 0.001343919717735509 8 0.0001553692118050011 10 1.864877345382558e-05 TEST030: BESSEL_KN_VALUES stores values of the Bessel Kn function. X KN(X) 2 0.2 49.51242928773287 2 1 1.624838898635177 2 2 0.2537597545660559 2 2.5 0.1214602062785638 2 3 0.06151045847174204 2 5 0.00530894371222346 2 10 2.150981700693277e-05 2 20 6.329543612292228e-10 3 1 7.101262824737945 3 2 0.6473853909486342 3 5 0.008291768415230933 3 10 2.725270025659869e-05 3 50 3.727936773826211e-23 5 1 360.9605896012407 5 2 9.431049100596468 5 5 0.03270627371203186 5 10 5.754184998531228e-05 5 50 4.367182254100986e-23 10 1 180713289.9010295 10 2 162482.4039795591 10 5 9.75856282917781 10 10 0.00161425530039067 10 50 9.150988209987996e-23 20 1 6.294369360424535e+22 20 2 5.770856852700241e+16 20 5 482700052.0621485 20 10 178.7442782077055 20 50 1.706148379722035e-21 TEST0305: BESSEL_KX_VALUES stores values of the Bessel Kn function for NONINTEGER order. X KN(X) 0.5 0.2 2.294489339798475 0.5 1 0.4610685044478946 0.5 2 0.1199377719680614 0.5 2.5 0.06506594315400999 0.5 3 0.03602598513176459 0.5 5 0.003776613374642883 0.5 10 1.799347809370518e-05 0.5 20 5.776373974707445e-10 1.5 1 0.9221370088957891 1.5 2 0.1799066579520922 1.5 5 0.004531936049571459 1.5 10 1.97928259030757e-05 1.5 50 3.486992497366216e-23 2.5 1 3.227479531135262 2.5 2 0.3897977588961997 2.5 5 0.006495775004385758 2.5 10 2.393132586462789e-05 2.5 50 3.627839645299048e-23 1.25 1 0.7311451879202114 1.25 2 0.1567475478393932 1.25 5 0.004257389528177461 1.25 10 1.915541065869563e-05 1.25 50 3.463337593569306e-23 2.75 1 4.731184839919541 2.75 2 0.4976876225514758 2.75 5 0.007300864610941163 2.75 10 2.546421294106458e-05 2.75 50 3.675275677913656e-23 TEST031: BESSEL_Y0_VALUES stores values of the Bessel Y0 function. X Y0(X) 0.1 -1.534238651350367 1 0.08825696421567696 2 0.5103756726497451 3 0.3768500100127904 4 -0.01694073932506499 5 -0.3085176252490338 6 -0.2881946839815792 7 -0.02594974396720926 8 0.2235214893875662 9 0.2499366982850247 10 0.05567116728359939 11 -0.1688473238920795 12 -0.2252373126343614 13 -0.07820786452787591 14 0.1271925685821837 15 0.2054642960389183 TEST032: BESSEL_Y0_INT_VALUES stores values of the integral of the Bessel Y0 function. X FX 0.001953125 -0.009144264286017211 0.0078125 -0.02968204739039759 0.125 -0.2539143127658539 0.5 -0.5617954559146403 1 -0.6370693766074231 2 -0.2821928500851009 4 0.3836696478531256 6 -0.1259506128579893 10 0.2412903183226668 16 0.1713806975762704 16.25 0.1895814262713408 17 0.1720384613644971 20 -0.1682159767721503 25 -0.09360792735142899 30 0.08822971194803665 40 -0.008932466273627416 50 -0.05481407100006349 70 -0.09495824600346638 100 -0.01959806485340497 125 -0.008308477235715477 TEST033: BESSEL_Y0_SPHERICAL_VALUES stores values of the spherical Bessel y0 function. X y0(X) 0.1 -9.950041652780259 0.2 -4.900332889206208 0.4 -2.302652485007213 0.6 -1.375559358182797 0.8 -0.8708833866839568 1 -0.5403023058681397 1.2 -0.301964795397228 1.4 -0.1214051020716007 1.6 0.01824970143830545 1.8 0.1262233859406039 2 0.2080734182735712 2.2 0.267500507843339 2.4 0.307247381475519 2.6 0.3295725974495951 2.8 0.3365079788102351 3 0.3299974988668152 3.2 0.3119671174358603 3.4 0.2843524095821944 3.6 0.2490995600928186 3.8 0.2081493978722149 4 0.163410905215903 TEST034: BESSEL_Y1_VALUES stores values of the Bessel Y1 function. X Y1(X) 0.1 -6.458951094702027 1 -0.7812128213002887 2 -0.1070324315409375 3 0.3246744247918 4 0.3979257105571 5 0.1478631433912268 6 -0.1750103443003983 7 -0.3026672370241849 8 -0.1580604617312475 9 0.1043145751967159 10 0.2490154242069539 11 0.1637055374149429 12 -0.05709921826089652 13 -0.2100814084206935 14 -0.1666448418561723 15 0.02107362803687351 TEST035: BESSEL_Y1_SPHERICAL_VALUES stores values of the spherical Bessel y1 function. X y1(X) 0.1 -100.4987506942709 0.2 -25.49501110000635 0.4 -6.730177068289658 0.6 -3.233669719296388 0.8 -1.985299346979349 1 -1.381773290676036 1.2 -1.028336567803712 1.4 -0.7906105943286149 1.6 -0.6133274385019998 1.8 -0.4709023582986618 2 -0.3506120042760553 2.2 -0.2459072254437506 2.4 -0.1534232496148467 2.6 -0.07151106706610352 2.8 0.0005427959479750482 3 0.06295916360231597 3.2 0.1157316440198251 3.4 0.1587922092967723 3.6 0.1921166676076864 3.8 0.2157913917934037 4 0.2300533501309578 TEST036: BESSEL_YN_VALUES stores values of the Bessel Yn function. X YN(X) 2 1 -1.650682606816254 2 2 -0.6174081041906827 2 5 0.3676628826055245 2 10 -0.005868082442208615 2 50 0.09579316872759649 5 1 -260.4058666258122 5 2 -9.935989128481975 5 5 -0.4536948224911019 5 10 0.1354030476893623 5 50 -0.07854841391308165 10 1 -121618014.2786892 10 2 -129184.5422080393 10 5 -25.1291100956101 10 10 -0.3598141521834027 10 50 0.005723897182053514 20 1 -4.113970314835505e+22 20 2 -4.081651388998367e+16 20 5 -593396529.6914321 20 10 -1597.483848269626 20 50 0.01644263394811578 TEST0365: BESSEL_YX_VALUES stores values of the Bessel Yn function for NONINTEGER order. X YN(X) 0.5 0.2 -1.748560416961876 0.5 1 -0.4310988680183761 0.5 2 0.2347857104062485 0.5 2.5 0.4042783022390569 0.5 3 0.4560488207946332 0.5 5 -0.1012177091851084 0.5 10 0.2117088663313982 0.5 20 -0.07280690478506185 1.5 1 -1.102495575160179 1.5 2 -0.3956232813587035 1.5 5 0.3219244429611401 1.5 10 0.1584346223881903 1.5 50 0.02742813676191382 2.5 1 -2.876387857462161 2.5 2 -0.8282206324443037 2.5 5 0.2943723749617925 2.5 10 -0.1641784796149411 2.5 50 0.1105304445562544 1.25 1 -0.9319659251969881 1.25 2 -0.2609445010948933 1.25 5 0.2492796362185881 1.25 10 0.2174410301416733 1.25 50 -0.01578576650557229 2.75 1 -4.023453301501028 2.75 2 -0.9588998694752389 2.75 5 0.2264260361047367 2.75 10 -0.219361773656676 2.75 50 0.09413988344515077 TEST037: BETA_CDF_VALUES stores values of the Beta CDF. A B X CDF(X) 0.5 0.5 0.01 0.06376856085851985 0.5 0.5 0.1 0.2048327646991335 0.5 0.5 1 1 1 0.5 0 0 1 0.5 0.01 0.005012562893380045 1 0.5 0.1 0.0513167019494862 1 0.5 0.5 0.2928932188134525 1 1 0.5 0.5 2 2 0.1 0.028 2 2 0.2 0.104 2 2 0.3 0.216 2 2 0.4 0.352 2 2 0.5 0.5 2 2 0.6 0.648 2 2 0.7 0.784 2 2 0.8 0.896 2 2 0.9 0.972 5.5 5 0.5 0.4361908850559777 10 0.5 0.9 0.1516409096347099 10 5 0.5 0.08978271484375 10 5 1 1 10 10 0.5 0.5 20 5 0.8 0.4598773297575791 20 10 0.6 0.2146816102371739 20 10 0.8 0.9507364826957875 20 20 0.5 0.5 20 20 0.6 0.8979413687105918 30 10 0.7 0.2241297491808366 30 10 0.8 0.7586405487192086 40 20 0.7 0.7001783247477069 1 0.5 0.1 0.0513167019494862 1 0.5 0.2 0.1055728090000841 1 0.5 0.3 0.1633399734659245 1 0.5 0.4 0.2254033307585166 1 2 0.2 0.36 1 3 0.2 0.488 1 4 0.2 0.5904 1 5 0.2 0.67232 2 2 0.3 0.216 3 2 0.3 0.0837 4 2 0.3 0.03078 5 2 0.3 0.010935 TEST038: BETA_INC_VALUES stores values of the incomplete Beta function. A B X BETA_INC(A,B)(X) 0.5 0.5 0.01 0.06376856085851985 0.5 0.5 0.1 0.2048327646991335 0.5 0.5 1 1 1 0.5 0 0 1 0.5 0.01 0.005012562893380045 1 0.5 0.1 0.0513167019494862 1 0.5 0.5 0.2928932188134525 1 1 0.5 0.5 2 2 0.1 0.028 2 2 0.2 0.104 2 2 0.3 0.216 2 2 0.4 0.352 2 2 0.5 0.5 2 2 0.6 0.648 2 2 0.7 0.784 2 2 0.8 0.896 2 2 0.9 0.972 5.5 5 0.5 0.4361908850559777 10 0.5 0.9 0.1516409096347099 10 5 0.5 0.08978271484375 10 5 1 1 10 10 0.5 0.5 20 5 0.8 0.4598773297575791 20 10 0.6 0.2146816102371739 20 10 0.8 0.9507364826957875 20 20 0.5 0.5 20 20 0.6 0.8979413687105918 30 10 0.7 0.2241297491808366 30 10 0.8 0.7586405487192086 40 20 0.7 0.7001783247477069 1 0.5 0.1 0.0513167019494862 1 0.5 0.2 0.1055728090000841 1 0.5 0.3 0.1633399734659245 1 0.5 0.4 0.2254033307585166 1 2 0.2 0.36 1 3 0.2 0.488 1 4 0.2 0.5904 1 5 0.2 0.67232 2 2 0.3 0.216 3 2 0.3 0.0837 4 2 0.3 0.03078 5 2 0.3 0.010935 TEST039: BETA_LOG_VALUES stores values of the logarithm of the Beta function. X Y BETA_LOG(X,Y) 0.2 1 1.6094379124341 0.4 1 0.9162907318741551 0.6 1 0.5108256237659907 0.8 1 0.2231435513142098 1 0.2 1.6094379124341 1 0.4 0.9162907318741551 1 1 0 2 2 -1.791759469228055 3 3 -3.401197381662155 4 4 -4.941642422609304 5 5 -6.445719819385578 6 2 -3.737669618283368 6 3 -5.123963979403259 6 4 -6.222576268071369 6 5 -7.138866999945524 6 6 -7.927324360309794 7 7 -9.39366142910322 TEST0395: BETA_NONCENTRAL_CDF_VALUES stores values of the noncentral Beta CDF. A B LAMBDA X CDF(X) 5 5 54 0.864 0.4563021 5 5 140 0.9 0.1041337 5 5 170 0.956 0.6022353 10 10 54 0.8686 0.918777 10 10 140 0.9 0.6008106 10 10 250 0.9 0.090285 20 20 54 0.8787 0.9998655 20 20 140 0.9 0.9925997 20 20 250 0.922 0.9641111999999999 10 20 150 0.868 0.9376626573 10 10 120 0.9 0.7306817858 15 5 80 0.88 0.1604256918 20 10 110 0.85 0.1867485313 20 30 65 0.66 0.6559386874000001 20 50 130 0.72 0.9796881486 30 20 80 0.72 0.1162386423 30 40 130 0.8 0.9930430054 10 5 20 0.644 0.0506899273 10 10 54 0.7 0.1030959706 10 30 80 0.78 0.9978417832000001 15 20 120 0.76 0.2555552369 10 5 55 0.795 0.0668307064 12 17 64 0.5600000000000001 0.0113601067 30 30 140 0.8 0.7813366615 35 30 20 0.67 0.8867126477 TEST040: BETA_VALUES stores values of the Beta function. X Y BETA(X,Y) 0.2 1 5 0.4 1 2.5 0.6 1 1.666666666666667 0.8 1 1.25 1 0.2 5 1 0.4 2.5 1 1 1 2 2 0.1666666666666667 3 3 0.03333333333333333 4 4 0.007142857142857143 5 5 0.001587301587301587 6 2 0.02380952380952381 6 3 0.005952380952380952 6 4 0.001984126984126984 6 5 0.0007936507936507937 6 6 0.0003607503607503608 7 7 8.325008325008325e-05 TEST041: BINOMIAL_VALUES returns values of the binomial numbers. A B C(A,B) 1 0 1 6 1 6 6 3 20 6 5 6 15 1 15 15 3 455 15 5 3003 15 7 6435 15 9 5005 15 11 1365 15 13 105 25 1 25 25 3 2300 25 5 53130 25 7 480700 25 9 2042975 25 11 4457400 25 13 5200300 25 15 3268760 25 17 1081575 TEST042: BINOMIAL_CDF_VALUES returns values of the Binomial Cumulative Density Function. A B X CDF(X) 2 0.05 0 0.9025 2 0.05 1 0.9975000000000001 2 0.05 2 1 2 0.5 0 0.25 2 0.5 1 0.75 4 0.25 0 0.31640625 4 0.25 1 0.73828125 4 0.25 2 0.94921875 4 0.25 3 0.99609375 10 0.05 4 0.9999363101685547 10 0.1 4 0.9983650626 10 0.15 4 0.9901259090013672 10 0.2 4 0.9672065023999999 10 0.25 4 0.9218730926513672 10 0.3 4 0.8497316673999999 10 0.4 4 0.6331032576 10 0.5 4 0.376953125 TEST0425: BIVARIATE_NORMAL_CDF_VALUES stores values of the bivariate normal CDF. R X Y F(R)(X,Y) 0.5 -2 1 0.023 0.5 -1 1 0.155 0.5 0 1 0.469 0.5 1 1 0.745 0.5 2 1 0.832 0.5 3 1 0.841 -0.9 -0.2 0.5 0.138 -0.8 -0.2 0.5 0.162 -0.7 -0.2 0.5 0.183 -0.6 -0.2 0.5 0.201 -0.5 -0.2 0.5 0.218 -0.4 -0.2 0.5 0.234 -0.3 -0.2 0.5 0.248 -0.2 -0.2 0.5 0.263 -0.1 -0.2 0.5 0.277 0 -0.2 0.5 0.291 0.1 -0.2 0.5 0.305 0.2 -0.2 0.5 0.318 0.3 -0.2 0.5 0.332 0.4 -0.2 0.5 0.346 0.5 -0.2 0.5 0.36 0.6 -0.2 0.5 0.374 0.7 -0.2 0.5 0.389 0.8 -0.2 0.5 0.403 0.9 -0.2 0.5 0.416 TEST043: 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 TEST044: CAUCHY_CDF_VALUES returns values of the Cauchy Cumulative Density Function. Mu Sigma X CDF(X) 1 0.5 1 0.5 1 0.5 2 0.8524163823495667 1 0.5 3 0.9220208696226307 1 0.5 4 0.9474315432887466 1 2 2 0.6475836176504333 1 3 2 0.6024163823495667 1 4 2 0.5779791303773693 1 5 2 0.5628329581890013 2 2 3 0.6475836176504333 3 2 3 0.5 4 2 3 0.3524163823495667 5 2 3 0.25 TEST0445: CBRT_VALUES stores values of the cube root function. X CBRT(X) 0 0 -8.100000073710001e-09 -0.002008298856338348 0.09 0.4481404746557165 -0.1 -0.4641588833612779 0.4 0.7368062997280773 -1 -1 2 1.259921049894873 -3 -1.442249570307408 3.141592653589793 1.464591887561523 -19 -2.668401648721945 29 3.072316825685847 -71 -4.140817749422853 97 4.594700892207039 -123456789 -497.9338592181745 TEST045: CHEBYSHEV_T_VALUES returns values of the Chebyshev T polynomials. N X T(N)(X) 0 0.8 1 1 0.8 0.8 2 0.8 0.28 3 0.8 -0.352 4 0.8 -0.8431999999999999 5 0.8 -0.99712 6 0.8 -0.752192 7 0.8 -0.2063872 8 0.8 0.42197248 9 0.8 0.881543168 10 0.8 0.9884965888 11 0.8 0.70005137408 12 0.8 0.131585609728 TEST046: CHEBYSHEV_U_VALUES returns values of the Chebyshev U polynomials. N X U(N)(X) 0 0.8 1 1 0.8 1.6 2 0.8 1.56 3 0.8 0.896 4 0.8 -0.1264 5 0.8 -1.09824 6 0.8 -1.630784 7 0.8 -1.5110144 8 0.8 -0.078683904 9 0.8 0.252071936 10 0.8 1.1901541376 11 0.8 1.65217468416 12 0.8 1.453325357056 TEST0465: CHI_VALUES stores values of the Hyperbolic Cosine Integral function CHI(X). X CHI(X) 0.5 -0.05277684495649362 0.6 0.1577508933739787 0.7 0.3455691756953907 0.8 0.5183999848333914 0.9 0.681313887185434 1 0.8378669409802082 1.2 1.141841924170595 1.4 1.445494075789644 1.6 1.759505807660965 1.8 2.092577214062032 2 2.452666922646915 2.5 3.524425488354165 3 4.96039209476561 3.5 6.959191927647393 4 9.813547558823187 4.5 13.96581164859243 TEST047: CHI_SQUARE_CDF_VALUES returns values of the Chi-Squared Cumulative Density Function. N X CDF(X) 1 0.01 0.07965567455405796 2 0.01 0.004987520807317687 1 0.02 0.1124629160182849 2 0.02 0.009950166250831945 1 0.4 0.4729107431344619 2 0.4 0.1812692469220181 3 0.4 0.05975750516063926 4 0.4 0.01752309630642177 1 1 0.6826894921370859 2 1 0.3934693402873666 3 1 0.1987480430987992 4 1 0.09020401043104986 5 1 0.03743422675270363 3 2 0.4275932955291202 3 3 0.6083748237289111 3 4 0.7385358700508894 3 5 0.8282028557032669 3 6 0.8883897749052874 10 1 0.0001721156299558408 10 2 0.003659846827343712 10 3 0.01857593622214067 TEST048: CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral Chi-Squared Cumulative Density Function. X LAMBDA DF CDF 3 0.5 1 0.8399444269398261 3 0.5 2 0.6959060300435139 3 0.5 3 0.5350879697078847 3 1 1 0.7647841496310313 3 1 2 0.6206436532195436 3 1 3 0.469166737537318 3 5 1 0.3070884345937569 3 5 2 0.2203818092990903 3 5 3 0.1500251895581519 3 20 1 0.003071163194335791 3 20 2 0.001763982670131894 3 20 3 0.0009816792594625021 60 30 60 0.01651753140866208 60 30 80 0.0002023419573950451 60 30 100 4.984476352854074e-07 0.05 5 1 0.01513252400654827 0.05 5 2 0.002090414910614367 0.05 5 3 0.0002465021206048452 4 2 10 0.02636835050342939 4 3 10 0.01857983220079215 4 4 10 0.0130573659548664 5 2 10 0.05838039534819351 5 3 10 0.04249784402463712 5 4 10 0.03082137716021596 6 2 10 0.1057878223400849 6 3 10 0.07940842984598509 6 4 10 0.05932010895599639 5 0.5 8 0.2110395656918684 TEST049: CI_VALUES stores values of the Cosine Integral function CI(X). X CI(X) 0.5 -0.1777840788066129 0.6 -0.02227070695927976 0.7 0.1005147070088978 0.8 0.1982786159524672 0.9 0.2760678304677729 1 0.3374039229009681 1.2 0.4204591828942405 1.4 0.4620065850946773 1.6 0.4717325169318778 1.8 0.4568111294183369 2 0.422980828774865 2.5 0.2858711963653835 3 0.1196297860080003 3.5 -0.03212854851248112 4 -0.1409816978869304 4.5 -0.1934911221017388 TEST050: CIN_VALUES stores values of the Cosine Integral function CIN(X). X CIN(X) 0.5 0.06185256314820045 0.6 0.08866074809482194 0.7 0.1200260139539026 0.8 0.1557934976348559 0.9 0.1957873187759337 1 0.2398117420005647 1.2 0.339078038801247 1.4 0.4516813164280685 1.6 0.5754867772153907 1.8 0.708191200385315 2 0.8473820166866132 2.5 1.207635200410304 3 1.556198167561642 3.5 1.862107181909382 4 2.104491723908354 4.5 2.274784183779546 TEST051: CLAUSEN_VALUES stores values of Clausen's integral function. X FX 0.001953125 0.01413735288676058 0.03125 0.1395546708198128 -0.125 -0.3849573215657424 0.5 0.8483118777036792 1 1.013959132360768 -1.5 -0.9392185927540921 2 0.7271460508632792 2.5 0.4335982032355328 -3 -0.09802620939130142 4 -0.5681439444298698 4.25 -0.7096970178444892 -5 0.9928201325469567 5.5 -0.9812774747744737 6 -0.6407826657017233 8 0.8602796373323119 -10 0.3907164760868021 15 0.4757479392653919 20 1.010501448141288 -30 0.9633208904436308 50 -0.6178269948192932 TEST05125: CLEBSCH_GORDAN_VALUES returns values of the Clebsch Gordan coefficient. J1 J2 J3 M1 M2 M3 CG 0.5 0.5 1 0.5 -0.5 -0.5 0.7071067811865475 0.5 0.5 1 0.5 0.5 0.5 1 0.5 1 1.5 -0.5 1 1 0.5773502691896258 1 1.5 1.5 0 0.5 0.5 -0.2581988897471611 1 1.5 1.5 -1 1.5 1.5 -0.6324555320336759 1 1.5 1.5 0 1.5 1.5 -0.7745966692414834 1 1 2 1 -1 -1 0.408248290463863 1 1 2 0 0 0 0.816496580927726 2 2 2 2 -2 -2 0.5345224838248488 2 2 2 1 -1 -1 0.2672612419124244 1.5 2 2.5 0.5 1 1 0.8944271909999159 1.5 2 3.5 1.5 -1 -1 0.3380617018914066 TEST0515: COLLATZ_COUNT_VALUES returns values of the length of the Collatz sequence that starts at N. N COLLATZ_COUNT(N) 1 1 2 2 3 8 4 3 5 6 6 9 7 17 8 4 9 20 10 7 27 112 50 25 100 26 200 27 300 17 400 28 500 111 600 18 700 83 800 29 TEST0517: COS_VALUES stores values of the cosine function. X FX 0 1 0.2617993877991495 0.9659258262890683 0.5 0.8775825618903728 0.5235987755982989 0.8660254037844386 0.7853981633974483 0.7071067811865476 1 0.5403023058681398 1.047197551196598 0.5 1.570796326794897 0 2 -0.4161468365471424 3 -0.9899924966004454 3.141592653589793 -1 4 -0.6536436208636119 5 0.2836621854632262 TEST0519: COSH_VALUES stores values of the hyperbolic cosine function. X FX -5 74.20994852478785 -1 1.543080634815244 0 1 0.1 1.005004168055804 0.2 1.020066755619076 0.3 1.04533851412886 0.4 1.081072371838455 0.5 1.127625965206381 0.6 1.185465218242268 0.7 1.255169005630943 0.8 1.337434946304844 0.9 1.433086385448774 1 1.543080634815244 2 3.762195691083631 3 10.06766199577777 4 27.30823283601649 5 74.20994852478785 10 11013.23292010332 TEST052: CP_VALUES stores values of the specific heat CP as a function of temperature and pressure. T P CP(T,P) 0 1 4.228 100 1 2.042 200 1 1.975 300 1 2.013 350 1 2.04 400 1 2.07 500 1 2.135 600 1 2.203 850 1 2.378 1100 1 2.541 1600 1 2.792 2000 1 2.931 0 5 4.226 0 10 4.223 0 50 4.202 0 100 4.177 0 200 4.13 0 300 4.089 0 400 4.053 0 500 4.021 0 1000 3.909 0 1500 3.844 0 2000 3.786 0 5000 2.89 TEST053: DAWSON_VALUES stores values of Dawson's integral function. X DAWSON(X) 0 0 0.1 0.09933599239785286 0.2 0.194751033368028 0.3 0.2826316650213119 0.4 0.3599434819348881 0.5 0.4244363835020223 0.6 0.4747632036629779 0.7 0.5105040575592318 0.8 0.5321017070563654 0.9 0.5407243187262987 1 0.5380795069127684 1.1 0.5262066799705525 1.2 0.5072734964077396 1.3 0.4833975173848241 1.4 0.4565072375268973 1.5 0.4282490710853986 1.6 0.3999398943230814 1.7 0.3725593489740788 1.8 0.3467727691148722 1.9 0.3229743193228178 2 0.301340388923792 TEST054: DEBYE1_VALUES stores values of the Debye function of order 1. X FX 0.001953125 0.9995118247138088 0.03125 0.992214626471206 0.125 0.9691839599789531 0.5 0.8819271567906055 1 0.7775046341122482 1.5 0.686145310789402 2 0.6069472846098101 2.5 0.5387895690778559 3 0.4804352195730429 4 0.3881480212979379 4.25 0.3693080282924253 5 0.3208761977001461 5.5 0.2942399662315425 6 0.2712604667850219 8 0.205239303102215 10 0.164443465679946 15 0.1096619448273582 20 0.08224670117820002 30 0.05483113556151085 50 0.03289868133696453 TEST055: DEBYE2_VALUES stores values of the Debye function of order 2. X FX 0.001953125 0.999349117279046 0.03125 0.9896240229959918 0.125 0.9589842620034599 0.5 0.8437211933472536 1 0.7078784756278292 1.5 0.5914963722567128 2 0.4930826439905319 2.5 0.4107941357974967 3 0.3426139606078635 4 0.240553687521279 4.25 0.2208277006120231 5 0.1723291593901414 5.5 0.1472434673873018 6 0.1266691904671579 8 0.07426880595486285 10 0.04797149802012187 15 0.02136920168365837 20 0.01202056447644643 30 0.005342475124953707 50 0.001923291045055351 TEST056: DEBYE3_VALUES stores values of the Debye function of order 3. X FX 0.001953125 0.9992677688598546 0.03125 0.988330077557347 0.125 0.9539061047202351 0.5 0.8249629689762337 1 0.6744155640778147 1.5 0.5471066514128629 2 0.4411284737276242 2.5 0.3541360348104239 3 0.2835798281434225 4 0.1817369138217748 4.25 0.1627792438511244 5 0.117597411799934 5.5 0.09524080272315889 6 0.07758132473376302 8 0.03656029567319485 10 0.01929576569034549 15 0.00577126322761888 20 0.002435220067480548 30 0.0007215488221633566 50 0.0001558545456544039 TEST057: DEBYE4_VALUES stores values of the Debye function of order 4. X FX 0.001953125 0.9992189619276157 0.03125 0.9875542528099607 0.125 0.9508678860638974 0.5 0.8138456917203404 1 0.6548740688867369 1.5 0.5216283096487871 2 0.4118927367178853 2.5 0.3229543485870731 3 0.2518786364288331 4 0.1518546125867202 4.25 0.1337266114592141 5 0.09147137766448117 5.5 0.07122782819746253 6 0.05567654782273886 8 0.02196756652557496 10 0.009673675560271159 15 0.001964697815835184 20 0.0006221464862396545 30 0.0001228951409207786 50 1.592721031900216e-05 TEST058: DIELECTRIC_VALUES stores values of the dielectric function. T P EPS(T,P) 0 100 88.29000000000001 0 500 90.06999999999999 0 1000 92.02 0 2000 95.14 0 5000 100.77 25 100 78.84999999999999 50 100 70.27 75 100 62.6 100 100 55.78 150 100 44.31 200 100 35.11 300 100 20.4 400 100 1.17 500 100 1.11 600 100 1.08 TEST059: DILOGARITHM_VALUES stores values of the dilogarithm function. X DILOGARITHM(X) 0 0 0.05 0.05063929246449603 0.1 0.1026177910993911 0.15 0.1560350339454831 0.2 0.2110037754397048 0.25 0.2676526390827326 0.3 0.3261295100754761 0.35 0.3866059411605865 0.4 0.4492829744712817 0.45 0.5143989891542119 0.5 0.5822405264650125 0.55 0.6531576315069018 0.6 0.7275863077163334 0.65 0.806082689517724 0.7 0.8893776242860387 0.75 0.9784693929303061 0.8 1.074794600008248 0.85 1.180581123830255 0.9 1.299714723004959 0.95 1.440633796970039 1 1.644934066848226 TEST060: E1_VALUES stores values of the exponential integral function E1(X). X E1(X) 0.5 0.5597735947761608 0.6 0.4543795031894021 0.7 0.3737688432335091 0.8 0.310596578545543 0.9 0.2601839393259996 1 0.2193839343955203 1.1 0.1859909045360402 1.2 0.1584084368514626 1.3 0.1354509578491291 1.4 0.1162193125713579 1.5 0.1000195824066327 1.6 0.08630833369753979 1.7 0.07465464440125305 1.8 0.06471312936386886 1.9 0.05620437817453485 2 0.04890051070806112 TEST061: EI_VALUES stores values of the exponential integral function EI(X). X EI(X) 0.5 0.4542199048631736 0.6 0.7698812899373594 0.7 1.064907194624291 0.8 1.347396548212326 0.9 1.622811713696867 1 1.895117816355937 1.1 2.167378279563403 1.2 2.442092285192652 1.3 2.721398880232024 1.4 3.007207464150646 1.5 3.301285449129798 1.6 3.605319949019469 1.7 3.920963201354904 1.8 4.249867557487934 1.9 4.593713686953585 2 4.95423435600189 TEST062: ELLIPTIC_EA_VALUES stores values of the complete elliptic integral of the second kind, with parameter angle ALPHA in degrees. ALPHA EA(ALPHA) 0 1.570796326794897 5 1.567809073977622 10 1.558887196601596 15 1.544150496914673 20 1.523799205259774 25 1.498114928422116 30 1.467462209339427 35 1.432290969306756 40 1.393140248523812 45 1.350643881047676 50 1.305539094297794 55 1.258679624779997 60 1.211056027568459 65 1.163827964493139 70 1.118377737969864 75 1.076405113076403 80 1.04011439570601 85 1.012663506234396 90 1 TEST063: ELLIPTIC_EM_VALUES stores values of the complete elliptic integral of the second kind, with parameter modulus M. M EM(M) 0 1.570796326794897 0.05 1.550973351780472 0.1 1.530757636897763 0.15 1.510121832092819 0.2 1.489035058095853 0.25 1.467462209339427 0.3 1.445363064412665 0.35 1.422691133490879 0.4 1.399392138897432 0.45 1.375401971871116 0.5 1.350643881047676 0.55 1.32502449795823 0.6 1.298428035046913 0.65 1.270707479650149 0.7 1.241670567945823 0.75 1.211056027568459 0.8 1.178489924327839 0.85 1.143395791883166 0.9 1.104774732704073 0.95 1.060473727766278 1 1 TEST064: ELLIPTIC_KA_VALUES stores values of the complete elliptic integral of the first kind, with parameter angle ALPHA in degrees. ALPHA KA(ALPHA) 0 1.570796326794897 5 1.573792130924768 10 1.582842804338351 15 1.59814200211254 20 1.620025899124204 25 1.64899521847853 30 1.685750354812596 35 1.731245175657058 40 1.786769134885021 45 1.854074677301372 50 1.935581096004722 55 2.034715312185791 60 2.156515647499643 65 2.308786798167196 70 2.504550079001634 75 2.768063145368768 80 3.153385251887839 85 3.831741999784146 TEST065: ELLIPTIC_KM_VALUES stores values of the complete elliptic integral of the first kind, with parameter modulus M. M KM(M) 0 1.570796326794897 0.05 1.591003453790792 0.1 1.612441348720219 0.15 1.63525673226458 0.2 1.659623598610528 0.25 1.685750354812596 0.3 1.713889448178791 0.35 1.744350597225613 0.4 1.777519371491253 0.45 1.813883936816983 0.5 1.854074677301372 0.55 1.898924910271554 0.6 1.949567749806026 0.65 2.007598398424376 0.7 2.075363135292469 0.75 2.156515647499643 0.8 2.257205326820854 0.85 2.38901648632558 0.9 2.578092113348173 0.95 2.908337248444552 TEST066: ERF_VALUES stores values of the error function ERF(X). X ERF(X) 0 0 0.1 0.1124629160182849 0.2 0.2227025892104785 0.3 0.3286267594591274 0.4 0.4283923550466685 0.5 0.5204998778130465 0.6 0.6038560908479259 0.7 0.6778011938374185 0.8 0.7421009647076605 0.9 0.7969082124228321 1 0.8427007929497149 1.1 0.8802050695740817 1.2 0.9103139782296354 1.3 0.9340079449406524 1.4 0.9522851197626488 1.5 0.9661051464753106 1.6 0.976348383344644 1.7 0.9837904585907746 1.8 0.9890905016357306 1.9 0.9927904292352575 2 0.9953222650189527 TEST0665: ERFC_VALUES stores values of the complementary error function ERFC(X). X ERFC(X) 0 1 0.2 0.7772974107895215 0.4 0.5716076449533315 0.6 0.3961439091520741 0.8 0.2578990352923395 1 0.1572992070502851 1.2 0.08968602177036462 1.4 0.04771488023735119 1.6 0.02365161665535599 1.8 0.01090949836426929 2 0.004677734981047266 2.2 0.001862846297981891 2.4 0.0006885138966450786 2.6 0.0002360344165293492 2.8 7.501319466545903e-05 3 2.209049699858544e-05 3.2 6.025761151762095e-06 3.4 1.521993362862285e-06 3.6 3.558629930076853e-07 3.8 7.700392745696413e-08 4 1.541725790028002e-08 TEST067: 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 TEST068: EULER_POLY_VALUES returns values of the Euler numbers. N X EULER_POLY(N)(X) 0 0.2 1 1 0.2 -0.3 2 0.2 -0.16 3 0.2 0.198 4 0.2 0.1856 5 0.2 -0.40368 6 0.2 -0.560896 7 0.2 1.7187888 8 0.2 3.18043136 9 0.2 -12.539467008 10 0.2 -28.9999384576 5 -0.5 -0.0625 5 -0.4 -0.17424 5 -0.3 -0.29768 5 -0.2 -0.40432 5 -0.1 -0.47526 5 0 -0.5 5 0.1 -0.47524 5 0.2 -0.40368 5 0.3 -0.29282 5 0.4 -0.15376 5 0.5 0 5 0.6 0.15376 5 0.7 0.29282 5 0.8 0.40368 5 0.9 0.47524 5 1 0.5 TEST0685: EXP_VALUES stores values of the exponential function. X FX -10 4.539992976248485e-05 -5 0.006737946999085467 -1 0.3678794411714423 0 1 1e-08 1.00000001 0.0001 1.000100005000167 0.001 1.001000500166708 0.01 1.010050167084168 0.1 1.105170918075648 0.2 1.22140275816017 0.3 1.349858807576003 0.4 1.49182469764127 0.5 1.648721270700128 0.6 1.822118800390509 0.7 2.013752707470477 0.8 2.225540928492467 0.9 2.45960311115695 1 2.718281828459045 2 7.38905609893065 3.141592653589793 23.14069263277927 5 148.4131591025766 10 22026.46579480672 20 485165195.4097903 40 2.3538526683702e+17 TEST069: EXP3_INT_VALUES stores values of the exponential integral function. X FX 0.001953125 0.001953124996362021 0.0078125 0.007812499068677552 0.03125 0.03124976158349973 0.125 0.1249389988880308 0.5 0.4849171431136397 1 0.8075111821396714 1.25 0.8688926541262327 1.5 0.8886172223535717 1.875 0.8928601850021818 2 0.8929535142938763 2.125 0.8929747911273784 2.25 0.8929788057979812 2.5 0.8929795031749662 2.75 0.892979511529519 3 0.8929795115691812 3.125 0.8929795115692474 3.25 0.8929795115692492 3.5 0.8929795115692493 3.75 0.8929795115692493 4 0.8929795115692493 TEST070: EXPONENTIAL_CDF_VALUES stores values of the exponential CDF. X FX 0.5 1 0.3934693402873666 0.5 2 0.6321205588285577 0.5 3 0.7768698398515702 0.5 4 0.8646647167633873 1 2 0.8646647167633873 2 2 0.9816843611112658 3 2 0.9975212478233336 4 2 0.9996645373720975 5 2 0.9999546000702375 TEST071: EXTREME_VALUES_CDF_VALUES stores values of the extreme values CDF. Alpha Beta X FX 1 0.5 1 0.3678794411714423 1 0.5 2 0.8734230184931167 1 0.5 3 0.9818510730616665 1 0.5 4 0.9975243173927525 1 2 2 0.545239211892605 1 3 2 0.4884435800065159 1 4 2 0.4589560693076638 1 5 2 0.4409910259429826 2 2 3 0.545239211892605 3 2 3 0.3678794411714423 4 2 3 0.1922956455479649 5 2 3 0.06598803584531254 TEST072: F_CDF_VALUES stores values of the F cumulative density function. A B X CDF(X) 1 1 1 0.5 1 5 0.528 0.4999714850534485 5 1 1.89 0.499603437017099 1 5 1.69 0.7496993658293228 2 10 1.6 0.7504656462757382 4 20 1.47 0.7514156325324275 1 5 4.06 0.8999867031372156 6 6 3.05 0.8997127554259698 8 16 2.09 0.9002845660853669 1 5 6.61 0.9500248817817623 3 10 3.71 0.9500574946122442 6 12 3 0.95019264 1 5 10.01 0.9750133887312993 1 5 16.26 0.9900022327445249 1 5 22.78 0.9949977837872073 1 5 47.18 0.9989999621122122 2 5 1 0.5687988496283078 3 5 1 0.5351452100063649 4 5 1 0.5143428032407864 5 5 1 0.5 TEST073: F_NONCENTRAL_CDF_VALUES stores values of the F cumulative density function. A B LAMBDA X CDF 1 1 0 1 0.5 1 5 0 1 0.6367825323508775 1 5 0.25 1 0.5840916116305482 1 5 1 0.5 0.3234431872392788 1 5 1 1 0.450118787981355 1 5 1 2 0.6078881441188312 1 5 1 3 0.7059275551414605 1 5 1 4 0.7721782003263727 1 5 1 5 0.8191049017635073 1 5 2 1 0.3170348430749965 2 5 1 1 0.4327218008454471 2 10 1 1 0.4502696915707327 3 5 1 1 0.4261881186594096 3 5 2 1 0.6753687206341544 4 5 1 1 0.4229108778879005 4 5 1 2 0.6927667261228938 5 1 0 1 0.3632174676491226 5 5 1 1 0.4210054012695865 6 6 1 1 0.4266672258818927 6 12 1 1 0.4464016600524644 8 16 1 2 0.8445888579504827 16 8 1 2 0.4339300273343604 TEST074: FRESNEL_COS_VALUES stores values of the Fresnel cosine integral C(X). X C(X) 0 0 0.2 0.1999210575944531 0.4 0.3974807591723594 0.6 0.5810954469916523 0.8 0.7228441718963561 1 0.7798934003768228 1.2 0.7154377229230734 1.4 0.5430957835462564 1.6 0.3654616834404877 1.8 0.3336329272215571 2 0.4882534060753408 2.2 0.6362860449033195 2.4 0.5549614058564281 2.6 0.388937496191969 2.8 0.4674916516989059 3 0.6057207892976856 TEST075: FRESNEL_SIN_VALUES stores values of the Fresnel sine integral S(X). X S(X) 0 0 0.2 0.004187609161656762 0.4 0.03335943266061318 0.6 0.110540207359387 0.8 0.2493413930539178 1 0.4382591473903548 1.2 0.6234009185462497 1.4 0.7135250773634121 1.6 0.6388876835093809 1.8 0.4509387692675831 2 0.3434156783636982 2.2 0.4557046121246569 2.4 0.6196899649456836 2.6 0.5499893231527195 2.8 0.3915284435431718 3 0.496312998967375 TEST0755: 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 TEST0756: FROBENIUS_NUMBER_ORDER_VALUES returns the order for a Frobenius problem; FROBENIUS_NUMBER_DATA_VALUES returns the corresponding coin denominations. Order = 2 2 5 Frobenius number = 3 Order = 2 3 17 Frobenius number = 31 Order = 2 4 19 Frobenius number = 53 Order = 2 5 13 Frobenius number = 47 Order = 2 12 11 Frobenius number = 109 Order = 2 99 100 Frobenius number = 9701 Order = 3 6 9 20 Frobenius number = 43 Order = 3 5 17 23 Frobenius number = 41 Order = 3 137 251 256 Frobenius number = 4948 Order = 4 31 41 47 61 Frobenius number = 240 Order = 4 271 277 281 283 Frobenius number = 13022 Order = 5 10 18 26 33 35 Frobenius number = 67 Order = 5 34 37 38 40 43 Frobenius number = 175 Order = 5 12223 12224 36674 61119 85569 Frobenius number = 89643481 Order = 6 1000 1476 3764 4864 4871 7773 Frobenius number = 47350 Order = 6 12228 36679 36682 46908 61139 73365 Frobenius number = 89716838 Order = 6 12137 36405 24269 36407 84545 60683 Frobenius number = 58925134 Order = 7 13211 13212 39638 66060 52864 79268 92482 Frobenius number = 104723595 Order = 8 13429 26850 26855 40280 40281 53711 53714 67141 Frobenius number = 45094583 TEST076: GAMMA_VALUES stores values of the Gamma function. X GAMMA(X) -0.5 -3.544907701811032 -0.01 -100.5871979644108 0.01 99.4325851191506 0.1 9.513507698668732 0.2 4.590843711998803 0.4 2.218159543757688 0.5 1.772453850905516 0.6 1.489192248812817 0.8 1.164229713725303 1 1 1.1 0.9513507698668732 1.2 0.9181687423997607 1.3 0.8974706963062772 1.4 0.8872638175030753 1.5 0.8862269254527581 1.6 0.8935153492876903 1.7 0.9086387328532904 1.8 0.9313837709802427 1.9 0.9617658319073874 2 1 3 2 4 6 10 362880 20 1.21645100408832e+17 30 8.841761993739702e+30 TEST077: GAMMA_CDF_VALUES stores values of the Gamma CDF. M Sigma X CDF((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 0.4421745996289254 3 2 3 0.1911531694619419 4 2 3 0.06564245437845009 5 2 3 0.01857593622214067 TEST078: GAMMA_INC_VALUES stores values of the incomplete Gamma function. A X GAMMA_INC(A)(X) 0.1 0.03 0.7382350532339351 0.1 0.3 0.9083579897300343 0.1 1.5 0.9886559833621947 0.5 0.075 0.3014646416966613 0.5 0.75 0.7793286380801532 0.5 3.5 0.9918490284064972 1 0.1 0.09516258196404043 1 1 0.6321205588285577 1 5 0.9932620530009145 1.1 0.1 0.07205974576054322 1.1 1 0.5891809618706485 1.1 5 0.9915368159845525 2 0.15 0.01018582711118352 2 1.5 0.4421745996289254 2 7 0.9927049442755639 6 2.5 0.04202103819530612 6 12 0.9796589705830716 11 16 0.9226039842296428 26 25 0.4470785799755852 41 45 0.7444549220718699 TEST079: GAMMA_LOG_VALUES stores values of the logarithm of the Gamma function. X GAMMA_LOG(X) 0.2 1.524063822430784 0.4 0.7966778177017837 0.6 0.3982338580692348 0.8 0.1520596783998375 1 0 1.1 -0.04987244125983972 1.2 -0.08537409000331583 1.3 -0.1081748095078604 1.4 -0.1196129141723712 1.5 -0.1207822376352452 1.6 -0.1125917656967557 1.7 -0.09580769740706586 1.8 -0.07108387291437215 1.9 -0.03898427592308333 2 0 3 0.6931471805599453 4 1.791759469228055 10 12.80182748008147 20 39.33988418719949 30 71.25703896716801 TEST080: GEGENBAUER_POLY_VALUES returns values of the Gegenbauer polynomials. N A X G(N,A)(X) 0 0.5 0.2 1 1 0.5 0.2 0.2 2 0.5 0.2 -0.44 3 0.5 0.2 -0.28 4 0.5 0.2 0.232 5 0.5 0.2 0.30752 6 0.5 0.2 -0.08057599999999999 7 0.5 0.2 -0.2935168 8 0.5 0.2 -0.0395648 9 0.5 0.2 0.2459712 10 0.5 0.2 0.1290720256 2 0 0.4 0 2 1 0.4 -0.36 2 2 0.4 -0.08 2 3 0.4 0.84 2 4 0.4 2.4 2 5 0.4 4.6 2 6 0.4 7.44 2 7 0.4 10.92 2 8 0.4 15.04 2 9 0.4 19.8 2 10 0.4 25.2 5 3 -0.5 -9 5 3 -0.4 -0.16128 5 3 -0.3 -6.67296 5 3 -0.2 -8.37504 5 3 -0.1 -5.52672 5 3 0 0 5 3 0.1 5.52672 5 3 0.2 8.37504 5 3 0.3 6.67296 5 3 0.4 0.16128 5 3 0.5 -9 5 3 0.6 -15.42528 5 3 0.7 -9.696960000000001 5 3 0.8 22.44096 5 3 0.9 100.88928 5 3 1 252 TEST081: GEOMETRIC_CDF_VALUES stores values of the Geometric Probability Cumulative Density Function. X P CDF 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 TEST082: GOODWIN_VALUES stores values of the Goodwin function. X FX 0.001953125 5.953154004044166 0.0078125 4.576960126862449 0.03125 3.228892133190222 0.125 1.974611087356872 0.5 0.9635604620869773 1 0.6051336525033446 1.25 0.513055064595322 1.5 0.4459860282094613 1.875 0.3734445820687975 2 0.3543359288495306 2.125 0.3371215651888192 2.5 0.2943617072936298 3 0.2519349964489722 3.5 0.2202877822212394 4 0.1957525823769892 4.5 0.176163031666707 5 0.1601546947966478 5.75 0.1409611687619339 6 0.1355498719104907 7 0.117516050600851 TEST083: GUD_VALUES stores values of the Gudermannian function. X GUD(X) -2 -1.301760336046015 -1 -0.8657694832396586 0 0 0.1 0.09983374879348662 0.2 0.1986798470079397 0.5 0.4803810791337294 1 0.8657694832396586 1.5 1.131728345250509 2 1.301760336046015 2.5 1.406993568936154 3 1.471304341117193 3.5 1.5104199075457 4 1.534169144334733 TEST084 HERMITE_POLY_VALUES stores values of the Hermite polynomials. N X H(N)(X) 0 5 1 1 5 10 2 5 98 3 5 940 4 5 8812 5 5 80600 6 5 717880 7 5 6211600 8 5 52065680 9 5 421271200 10 5 3275529760 11 5 24329873600 12 5 171237081280 5 0.5 41 5 1 -8 5 3 3816 5 10 3041200 TEST0845: HYPER_2F1_VALUES stores values of the hypergeometric function 2F1. A B C X Hyper_2F1(A,B,C,X) -2.5 3.3 6.7 0.25 0.7235612934899779 -0.5 1.1 6.7 0.25 0.9791110934527796 0.5 1.1 6.7 0.25 1.021657814008856 2.5 3.3 6.7 0.25 1.405156320011213 -2.5 3.3 6.7 0.55 0.4696143163982161 -0.5 1.1 6.7 0.55 0.9529619497744632 0.5 1.1 6.7 0.55 1.051281421394799 2.5 3.3 6.7 0.55 2.399906290477786 -2.5 3.3 6.7 0.85 0.2910609592841472 -0.5 1.1 6.7 0.85 0.9253696791037318 0.5 1.1 6.7 0.85 1.0865504094807 2.5 3.3 6.7 0.85 5.738156552618904 3.3 6.7 -5.5 0.25 15090.66974870461 1.1 6.7 -0.5 0.25 -104.3117006736435 1.1 6.7 0.5 0.25 21.17505070776881 3.3 6.7 4.5 0.25 4.194691581903192 3.3 6.7 -5.5 0.55 10170777974.04881 1.1 6.7 -0.5 0.55 -24708.63532248916 1.1 6.7 0.5 0.55 1372.230454838499 3.3 6.7 4.5 0.55 58.09272870639465 3.3 6.7 -5.5 0.85 5.868208761512417e+18 1.1 6.7 -0.5 0.85 -446350101.47296 1.1 6.7 0.5 0.85 5383505.756129573 3.3 6.7 4.5 0.85 20396.91377601966 TEST085: HYPERGEOMETRIC_CDF_VALUES stores values of the Hypergeometric CDF. SAM SUC POP X HyperCDF(S,S,P)(X) 10 90 100 7 0.06001858177500578 10 90 100 8 0.2615284665839845 10 90 100 9 0.6695237889132748 10 90 100 10 1 6 90 100 6 1 7 90 100 6 0.5332595856827856 8 90 100 6 0.181949596411764 9 90 100 6 0.0444804701752773 10 10 100 6 0.9999991751316731 10 30 100 6 0.992686089656075 10 50 100 6 0.8410799901444538 10 70 100 6 0.3459800113391901 10 90 90 0 0 10 90 200 0 0.002088888139634505 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 TEST0855: HYPERGEOMETRIC_PDF_VALUES stores values of the Hypergeometric PDF. SAM SUC POP X HyperPDF(S,S,P)(X) 10 90 100 7 0.05179370533242827 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 0.150561423973295 9 90 100 6 0.03927689321042477 10 10 100 6 3.099828465518108e-05 10 30 100 6 0.03145116093938197 10 50 100 6 0.2114132170316862 10 70 100 6 0.207577662199921 10 90 90 0 0 10 90 200 0 0.002088888139634505 10 90 1000 0 0.3876752992448843 10 90 10000 0 0.9135215248834896 TEST086: I4_FACTORIAL_VALUES return;s values of the factorial function. N N! 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3628800 11 39916800 12 479001600 TEST087: I4_FACTORIAL2_VALUES return;s 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 TEST088: I4_POCHHAMMER_VALUES returns some exact values of the Pochhammer symbol: M N Pochhammer(M,N) 50 0 1 10 1 10 4000 1 4000 10 2 110 18 3 6840 4 4 840 98 3 970200 1 7 5040 TEST089: I0ML0_VALUES stores values of the I0-L0 function. X FX 0.001953125 0.9987575551546175 0.015625 0.9901135823070665 0.125 0.9241943531002395 0.5 0.7362426713471427 1 0.5558226918141175 2 0.3421515443446216 4 0.1708717488877471 8 0.08108100870921921 12 0.05344942144108958 16 0.03995032100892325 16.25 0.03933063743758492 17 0.03758227434280867 20 0.03191248655448039 25 0.02550614688350474 30 0.02124448031782529 40 0.01592549834855168 50 0.01273750692724259 75 0.008489775081478492 100 0.006366834917845447 125 0.005093284316312255 TEST090: I1ML1_VALUES stores values of the I1-L1 function. X FX 0.001953125 0.0009757534615538627 0.015625 0.007760929328060927 0.125 0.05930296640454537 0.5 0.2039521227673737 1 0.3383947229366764 2 0.4878770672696132 4 0.5901873419657652 8 0.6260453953031215 12 0.6320931527490976 16 0.6341017931323536 16.25 0.6341796679757813 17 0.6343926863239209 20 0.6350157907325777 25 0.6355961667735945 30 0.6359100182669711 40 0.6362211318175107 50 0.6363648170213361 75 0.636506534996199 100 0.6365560912630026 125 0.6365790208718393 TEST091: JACOBI_CN_VALUES returns values of the Jacobi elliptic CN function. A X CN(A,X) 0 0.1 0.9950041652780258 0 0.2 0.9800665778412416 0 0.5 0.8775825618903726 0 1 0.5403023058681397 0 2 -0.4161468365471424 0.5 0.1 0.9950124626090582 0.5 0.2 0.9801976276784098 0.5 0.5 0.8822663948904403 0.5 1 0.5959765676721407 0.5 2 -0.1031836155277618 1 0.1 0.9950207489532265 1 0.2 0.9803279976447253 1 0.5 0.8868188839700739 1 1 0.6480542736638853 1 2 0.2658022288340797 1 4 0.03661899347368653 1 -0.2 0.9803279976447253 1 -0.5 0.8868188839700739 1 -1 0.6480542736638853 1 -2 0.2658022288340797 TEST092: JACOBI_DN_VALUES returns values of the Jacobi elliptic DN function. A X DN(A,X) 0 0.1 1 0 0.2 1 0 0.5 1 0 1 1 0 2 1 0.5 0.1 0.9975093485144243 0.5 0.2 0.9901483195224799 0.5 0.5 0.9429724257773857 0.5 1 0.8231610016315963 0.5 2 0.7108610477840873 1 0.1 0.9950207489532265 1 0.2 0.9803279976447253 1 0.5 0.8868188839700739 1 1 0.6480542736638853 1 2 0.2658022288340797 1 4 0.03661899347368653 1 -0.2 0.9803279976447253 1 -0.5 0.8868188839700739 1 -1 0.6480542736638853 1 -2 0.2658022288340797 TEST093: JACOBI_POLY_VALUES returns values of the Jacobi polynomial. N A B X J(N,A,B)(X) 0 0 1 0.5 1 1 0 1 0.5 0.25 2 0 1 0.5 -0.375 3 0 1 0.5 -0.484375 4 0 1 0.5 -0.1328125 5 0 1 0.5 0.275390625 5 1 1 0.5 -0.1640625 5 2 1 0.5 -1.1748046875 5 3 1 0.5 -2.361328125 5 4 1 0.5 -2.6162109375 5 5 1 0.5 0.1171875 5 0 2 0.5 0.421875 5 0 3 0.5 0.5048828125 5 0 4 0.5 0.509765625 5 0 5 0.5 0.4306640625 5 0 1 -1 -6 5 0 1 -0.8 0.03862 5 0 1 -0.6 0.81184 5 0 1 -0.4 0.03666 5 0 1 -0.2 -0.48512 5 0 1 0 -0.3125 5 0 1 0.2 0.18912 5 0 1 0.4 0.40234 5 0 1 0.6 0.01216 5 0 1 0.8 -0.43962 5 0 1 1 1 TEST094: JACOBI_SN_VALUES returns values of the Jacobi elliptic SN function. A X SN(A,X) 0 0.1 0.09983341664682815 0 0.2 0.1986693307950612 0 0.5 0.479425538604203 0 1 0.8414709848078965 0 2 0.9092974268256817 0.5 0.1 0.09975068547462485 0.5 0.2 0.1980217429819704 0.5 0.5 0.4707504736556573 0.5 1 0.8030018248956439 0.5 2 0.9946623253580177 1 0.1 0.09966799462495582 1 0.2 0.197375320224904 1 0.5 0.4621171572600098 1 1 0.7615941559557649 1 2 0.9640275800758169 1 4 0.999329299739067 1 -0.2 -0.197375320224904 1 -0.5 -0.4621171572600098 1 -1 -0.7615941559557649 1 -2 -0.9640275800758169 TEST0945: JED_CE_VALUES returns: JED, a Julian Ephemeris Date, and YMDF, the corresponding year, month, day, fraction. JED Y M D F 0 -4713 1 1 0.5 1 -4713 1 2 0.5 259261 -4004 10 26 0.5 347998.5 -3761 10 8 0 584282.5 -3114 9 6 0 588465.75 -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