25 June 2018 03:30:43 PM TEST_VALUES_TEST: C++ version, Test the TEST_VALUES library. ABRAM0_VALUES_TEST: 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 ABRAM1_VALUES_TEST: 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 ABRAM2_VALUES_TEST: 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 AGM_VALUES_TEST: 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 AIRY_AI_VALUES_TEST: 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 AIRY_AI_INT_VALUES_TEST: 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 AIRY_AI_PRIME_VALUES_TEST: 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 AIRY_BI_VALUES_TEST: 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 AIRY_BI_INT_VALUES_TEST: 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 AIRY_BI_PRIME_VALUES_TEST: 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 AIRY_CAI_VALUES_TEST: 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 AIRY_CBI_VALUES_TEST: 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 AIRY_GI_VALUES_TEST: 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 AIRY_HI_VALUES_TEST: 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 ARCCOS_VALUES_TEST: 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 ARCCOSH_VALUES_TEST: 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 ARCSIN_VALUES_TEST: 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 ARCSINH_VALUES_TEST: 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 ARCTAN_VALUES_TEST: 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 ARCTAN_INT_VALUES_TEST: 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 ARCTANH_VALUES_TEST: 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 BEI0_VALUES_TEST: 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 BEI1_VALUES_TEST: 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 BELL_VALUES_TEST: BELL_VALUES returns values of the Bell numbers. N BELL(N) 0 1 1 1 2 2 3 5 4 15 5 52 6 203 7 877 8 4140 9 21147 10 115975 BER0_VALUES_TEST: BER0_VALUES stores values of the Kelvin function BER of order 0. X FX 0 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 BER1_VALUES_TEST: 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 BERNOULLI_NUMBER_VALUES_TEST: 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 BERNOULLI_POLY_VALUES_TEST: 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 0.00666667 3 0.2 0.048 4 0.2 -0.00773333 5 0.2 -0.02368 6 0.2 0.00691352 7 0.2 0.0249088 8 0.2 -0.01015 9 0.2 -0.0452782 10 0.2 0.0233263 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 BERNSTEIN_POLY_01_VALUES_TEST: BERNSTEIN_POLY_01_VALUES returns values of the Bernstein Polynomials. N K X BERNSTEIN(N,K)(X) 0 0 0.25 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 0.316406 4 1 0.25 0.421875 4 2 0.25 0.210938 4 3 0.25 0.046875 4 4 0.25 0.00390625 BESSEL_I0_VALUES_TEST: BESSEL_I0_VALUES stores values of the Bessel I0 function. X I0(X) 0 1 0.2 1.01003 0.4 1.0404 0.6 1.09205 0.8 1.16651 1 1.26607 1.2 1.39373 1.4 1.5534 1.6 1.74998 1.8 1.98956 2 2.27959 2.5 3.28984 3 4.88079 3.5 7.3782 4 11.3019 4.5 17.4812 5 27.2399 6 67.2344 8 427.564 10 2815.72 BESSEL_I0_INT_VALUES_TEST: 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 BESSEL_I0_SPHERICAL_VALUES_TEST: BESSEL_I0_SPHERICAL_VALUES stores values of the spherical Bessel i0 function. X i0(X) 0.1 1.00167 0.2 1.00668 0.4 1.02688 0.6 1.06109 0.8 1.11013 1 1.1752 1.2 1.25788 1.4 1.36022 1.6 1.48473 1.8 1.63454 2 1.81343 2.2 2.02596 2.4 2.2776 2.6 2.5749 2.8 2.92569 3 3.33929 3.2 3.82684 3.4 4.40158 3.6 5.07929 3.8 5.87879 4 6.82248 BESSEL_I1_VALUES_TEST: BESSEL_I1_VALUES stores values of the Bessel I1 function. X I1(X) 0 0 0.2 0.100501 0.4 0.204027 0.6 0.313704 0.8 0.432865 1 0.565159 1.2 0.714678 1.4 0.886092 1.6 1.08481 1.8 1.31717 2 1.59064 2.5 2.51672 3 3.95337 3.5 6.20583 4 9.75947 4.5 15.3892 5 24.3356 6 61.3419 8 399.873 10 2670.99 BESSEL_I1_SPHERICAL_VALUES_TEST: BESSEL_I1_SPHERICAL_VALUES stores values of the spherical Bessel i1 function. X i1(X) 0.1 0.0333667 0.2 0.0669337 0.4 0.135479 0.6 0.207293 0.8 0.284128 1 0.367879 1.2 0.460643 1.4 0.564774 1.6 0.682959 1.8 0.818296 2 0.974383 2.2 1.15543 2.4 1.3664 2.6 1.61312 2.8 1.90252 3 2.24279 3.2 2.64369 3.4 3.11681 3.6 3.67597 3.8 4.33763 4 5.12144 BESSEL_IN_VALUES_TEST: BESSEL_IN_VALUES stores values of the Bessel In function. N X IN(X) 2 0.2 0.00501669 2 1 0.135748 2 2 0.688948 2 2.5 1.27647 2 3 2.24521 2 5 17.5056 2 10 2281.52 2 20 3.93128e+07 3 1 0.0221684 3 2 0.21274 3 5 10.3312 3 10 1758.38 3 50 2.67776e+20 5 1 0.000271463 5 2 0.00982568 5 5 2.15797 5 10 777.188 5 50 2.27855e+20 10 1 2.75295e-10 10 2 3.01696e-07 10 5 0.00458004 10 10 21.8917 10 50 1.0716e+20 20 1 3.96684e-25 20 2 4.31056e-19 20 5 5.02424e-11 20 10 0.00012508 20 50 5.44201e+18 BESSEL_IX_VALUES_TEST: BESSEL_IX_VALUES stores values of the Bessel In function for NONINTEGER order. NU X IN(X) 0.5 0.2 0.359208 0.5 1 0.937675 0.5 2 2.04624 0.5 2.5 3.05309 0.5 3 4.61482 0.5 5 26.4775 0.5 10 2778.78 0.5 20 4.32797e+07 1.5 1 0.293525 1.5 2 1.09947 1.5 5 21.1844 1.5 10 2500.91 1.5 50 2.86665e+20 2.5 1 0.0570989 2.5 2 0.397027 2.5 5 13.7669 2.5 10 2028.51 2.5 50 2.75316e+20 1.25 1 0.413942 1.25 2 1.3402 1.25 5 22.8572 1.25 10 2593.01 1.25 50 2.88663e+20 2.75 1 0.0359091 2.75 2 0.293111 2.75 5 11.994 2.75 10 1894.58 2.75 50 2.71691e+20 BESSEL_J_SPHERICAL_VALUES_TEST: BESSEL_J_SPHERICAL_VALUES stores values of the spherical Bessel jn function. N X jn(X) 0 0.905 0.868978 1 0.905 0.277671 2 0.905 0.0514791 3 0.905 0.00674393 4 0.905 0.000683829 5 0.905 5.6586e-05 6 0.905 3.95592e-06 7 0.905 2.39445e-07 8 0.905 1.27794e-08 9 0.905 6.09957e-10 10 0.905 2.6331e-11 0 10 -0.0544021 1 10 0.0784669 2 10 0.0779422 3 10 -0.0394958 4 10 -0.105589 5 10 -0.0555345 6 10 0.0445013 7 10 0.113386 8 10 0.125578 9 10 0.100096 10 10 0.0646052 BESSEL_J0_VALUES_TEST: BESSEL_J0_VALUES stores values of the Bessel J0 function. X J0(X) -5 -0.177597 -4 -0.39715 -3 -0.260052 -2 0.223891 -1 0.765198 0 1 1 0.765198 2 0.223891 3 -0.260052 4 -0.39715 5 -0.177597 6 0.150645 7 0.300079 8 0.171651 9 -0.0903336 10 -0.245936 11 -0.17119 12 0.0476893 13 0.206926 14 0.171073 15 -0.0142245 BESSEL_J0_INT_VALUES_TEST: 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 BESSEL_J0_SPHERICAL_VALUES_TEST: BESSEL_J0_SPHERICAL_VALUES stores values of the spherical Bessel j0 function. X j0(X) 0.1 0.998334 0.2 0.993347 0.4 0.973546 0.6 0.941071 0.8 0.896695 1 0.841471 1.2 0.776699 1.4 0.703893 1.6 0.624734 1.8 0.541026 2 0.454649 2.2 0.367498 2.4 0.281443 2.6 0.19827 2.8 0.119639 3 0.04704 3.2 -0.0182419 3.4 -0.0751591 3.6 -0.122922 3.8 -0.161015 4 -0.189201 BESSEL_J0_ZERO_VALUES_TEST: BESSEL_J0_ZERO_VALUES stores values of zeros of the Bessel J0 function. K X(K) 1 2.40483 2 5.52008 3 8.65373 4 11.7915 5 14.9309 6 18.0711 7 21.2116 8 24.3525 9 27.4935 10 30.6346 11 33.7758 12 36.9171 13 40.0584 14 43.1998 15 46.3412 16 49.4826 17 52.6241 18 55.7655 19 58.907 20 62.0485 21 65.19 22 68.3315 23 71.473 24 74.6145 25 77.756 26 80.8976 27 84.0391 28 87.1806 29 90.3222 30 93.4637 BESSEL_J1_VALUES_TEST: BESSEL_J1_VALUES stores values of the Bessel J1 function. X J1(X) -5 0.327579 -4 0.0660433 -3 -0.339059 -2 -0.576725 -1 -0.440051 0 0 1 0.440051 2 0.576725 3 0.339059 4 -0.0660433 5 -0.327579 6 -0.276684 7 -0.00468282 8 0.234636 9 0.245312 10 0.0434727 11 -0.176785 12 -0.223447 13 -0.0703181 14 0.133375 15 0.205104 BESSEL_J1_SPHERICAL_VALUES_TEST: BESSEL_J1_SPHERICAL_VALUES stores values of the spherical Bessel j1 function. X j1(X) 0.1 0.0333 0.2 0.0664004 0.4 0.131212 0.6 0.192892 0.8 0.249986 1 0.301169 1.2 0.345285 1.4 0.381375 1.6 0.408708 1.8 0.426794 2 0.435398 2.2 0.434545 2.4 0.424515 2.6 0.40583 2.8 0.379236 3 0.345677 3.2 0.306267 3.4 0.262247 3.6 0.214954 3.8 0.165777 4 0.116111 BESSEL_JN_VALUES_TEST: BESSEL_JN_VALUES stores values of the Bessel Jn function. N X JN(X) 2 1 0.114903 2 2 0.352834 2 5 0.0465651 2 10 0.25463 2 50 -0.0597128 5 1 0.000249758 5 2 0.00703963 5 5 0.261141 5 10 -0.234062 5 50 -0.0814002 10 1 2.63062e-10 10 2 2.51539e-07 10 5 0.0014678 10 10 0.207486 10 50 -0.113848 20 1 3.8735e-25 20 2 3.91897e-19 20 5 2.77033e-11 20 10 1.15134e-05 20 50 -0.116704 BESSEL_JX_VALUES_TEST: BESSEL_JX_VALUES stores values of the Bessel Jn function for NONINTEGER order. NU X JN(X) 0.5 0.2 0.354451 0.5 1 0.671397 0.5 2 0.513016 0.5 2.5 0.302005 0.5 3 0.0650082 0.5 5 -0.342168 0.5 10 -0.137264 0.5 20 0.162881 1.5 1 0.240298 1.5 2 0.491294 1.5 5 -0.169651 1.5 10 0.197982 1.5 50 -0.109477 2.5 1 0.0494968 2.5 2 0.223925 2.5 5 0.240377 2.5 10 0.196658 2.5 50 0.0230372 1.25 1 0.331415 1.25 2 0.546173 1.25 5 -0.261658 1.25 10 0.129604 1.25 50 -0.111743 2.75 1 0.0314262 2.75 2 0.171792 2.75 5 0.312663 2.75 10 0.134029 2.75 50 0.0623597 BESSEL_K0_VALUES_TEST: BESSEL_K0_VALUES stores values of the Bessel K0 function. X K0(X) 0.1 2.42707 0.2 1.7527 0.4 1.11453 0.6 0.777522 0.8 0.565347 1 0.421024 1.2 0.318508 1.4 0.243655 1.6 0.187955 1.8 0.145931 2 0.113894 2.5 0.0623476 3 0.0347395 3.5 0.0195989 4 0.0111597 4.5 0.00639986 5 0.0036911 6 0.00124399 8 0.000146471 10 1.77801e-05 BESSEL_K0_INT_VALUES_TEST: 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 BESSEL_K1_VALUES_TEST: BESSEL_K1_VALUES stores values of the Bessel K1 function. X K1(X) 0.1 9.85384 0.2 4.77597 0.4 2.18435 0.6 1.30283 0.8 0.861782 1 0.601907 1.2 0.434592 1.4 0.320836 1.6 0.240634 1.8 0.182623 2 0.139866 2.5 0.0738908 3 0.0401564 3.5 0.0222394 4 0.0124835 4.5 0.00707809 5 0.00404461 6 0.00134392 8 0.000155369 10 1.86488e-05 BESSEL_KN_VALUES_TEST: BESSEL_KN_VALUES stores values of the Bessel Kn function. N X KN(X) 2 0.2 49.5124 2 1 1.62484 2 2 0.25376 2 2.5 0.12146 2 3 0.0615105 2 5 0.00530894 2 10 2.15098e-05 2 20 6.32954e-10 3 1 7.10126 3 2 0.647385 3 5 0.00829177 3 10 2.72527e-05 3 50 3.72794e-23 5 1 360.961 5 2 9.43105 5 5 0.0327063 5 10 5.75418e-05 5 50 4.36718e-23 10 1 1.80713e+08 10 2 162482 10 5 9.75856 10 10 0.00161426 10 50 9.15099e-23 20 1 6.29437e+22 20 2 5.77086e+16 20 5 4.827e+08 20 10 178.744 20 50 1.70615e-21 BESSEL_KX_VALUES_TEST: BESSEL_KX_VALUES stores values of the Bessel Kn function for NONINTEGER order. NU X KN(X) 0.5 0.2 2.29449 0.5 1 0.461069 0.5 2 0.119938 0.5 2.5 0.0650659 0.5 3 0.036026 0.5 5 0.00377661 0.5 10 1.79935e-05 0.5 20 5.77637e-10 1.5 1 0.922137 1.5 2 0.179907 1.5 5 0.00453194 1.5 10 1.97928e-05 1.5 50 3.48699e-23 2.5 1 3.22748 2.5 2 0.389798 2.5 5 0.00649578 2.5 10 2.39313e-05 2.5 50 3.62784e-23 1.25 1 0.731145 1.25 2 0.156748 1.25 5 0.00425739 1.25 10 1.91554e-05 1.25 50 3.46334e-23 2.75 1 4.73118 2.75 2 0.497688 2.75 5 0.00730086 2.75 10 2.54642e-05 2.75 50 3.67528e-23 BESSEL_Y0_VALUES_TEST: BESSEL_Y0_VALUES stores values of the Bessel Y0 function. X Y0(X) 0.1 -1.53424 1 0.088257 2 0.510376 3 0.37685 4 -0.0169407 5 -0.308518 6 -0.288195 7 -0.0259497 8 0.223521 9 0.249937 10 0.0556712 11 -0.168847 12 -0.225237 13 -0.0782079 14 0.127193 15 0.205464 BESSEL_Y0_INT_VALUES_TEST: 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 BESSEL_Y0_SPHERICAL_VALUES_TEST: 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 BESSEL_Y1_VALUES_TEST: 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 BESSEL_Y1_SPHERICAL_VALUES_TEST: 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 BESSEL_YN_VALUES_TEST: BESSEL_YN_VALUES stores values of the Bessel Yn function. N X YN(X) 2 1 -1.65068 2 2 -0.617408 2 5 0.367663 2 10 -0.00586808 2 50 0.0957932 5 1 -260.406 5 2 -9.93599 5 5 -0.453695 5 10 0.135403 5 50 -0.0785484 10 1 -1.21618e+08 10 2 -129185 10 5 -25.1291 10 10 -0.359814 10 50 0.0057239 20 1 -4.11397e+22 20 2 -4.08165e+16 20 5 -5.93397e+08 20 10 -1597.48 20 50 0.0164426 BESSEL_YX_VALUES_TEST: BESSEL_YX_VALUES stores values of the Bessel Yn function for NONINTEGER order. NU X YN(X) 0.5 0.2 -1.74856 0.5 1 -0.431099 0.5 2 0.234786 0.5 2.5 0.404278 0.5 3 0.456049 0.5 5 -0.101218 0.5 10 0.211709 0.5 20 -0.0728069 1.5 1 -1.1025 1.5 2 -0.395623 1.5 5 0.321924 1.5 10 0.158435 1.5 50 0.0274281 2.5 1 -2.87639 2.5 2 -0.828221 2.5 5 0.294372 2.5 10 -0.164178 2.5 50 0.11053 1.25 1 -0.931966 1.25 2 -0.260945 1.25 5 0.24928 1.25 10 0.217441 1.25 50 -0.0157858 2.75 1 -4.02345 2.75 2 -0.9589 2.75 5 0.226426 2.75 10 -0.219362 2.75 50 0.0941399 BETA_VALUES_TEST: 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 BETA_CDF_VALUES_TEST: 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 1.30625 11.7562 0.225609 0.918884684620518 1.30625 11.7562 0.0335568 0.21052977489419 1.30625 11.7562 0.0295222 0.1824130512500673 BETA_INC_VALUES_TEST: BETA_INC_VALUES stores values of the incomplete Beta function. A B X BETA_INC(A,B)(X) 0.5 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 1.30625 11.7562 0.225609 0.918884684620518 1.30625 11.7562 0.0335568 0.21052977489419 1.30625 11.7562 0.0295222 0.1824130512500673 BETA_LOG_VALUES_TEST: BETA_LOG_VALUES stores values of the logarithm of the Beta function. X Y BETA_LOG(X,Y) 0.2 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 BETA_NONCENTRAL_CDF_VALUES_TEST: 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 BETA_PDF_VALUES_TEST: BETA_PDF_VALUES stores values of the Beta PDF. ALPHA BETA X PDF(X) 1.09209 4.78159 0.866722 0.002826137156803199 2.808477213834471 2.076535407379806 0.04607764003473368 0.04208950342768649 1.287888961910225 0.549783967662353 0.02211617261254013 0.2184064957817208 3.169828561512062 0.3086361453280091 0.4582543823302144 0.1335142301445414 2.006531407488083 3.773367432107051 0.8320834756642252 0.1070571849830009 0.009191855792026001 4.487520304498656 0.3520587633290876 0.005796394377470491 0.472723751058401 0.06808445791730976 0.898529119425846 0.5518796772414584 4.204237253278341 0.6155195788227712 -0.01692420862048847 0 1.301514988836825 4.562418534907164 0.09718884992568674 2.87907465409348 1.758143299519481 4.114436583429598 0.2621671905296927 2.126992854611924 BINOMIAL_VALUES_TEST: BINOMIAL_VALUES returns values of the binomial numbers. A B C(A,B) 1 0 1 6 1 6 6 3 20 6 5 6 15 1 15 15 3 455 15 5 3003 15 7 6435 15 9 5005 15 11 1365 15 13 105 25 1 25 25 3 2300 25 5 53130 25 7 480700 25 9 2042975 25 11 4457400 25 13 5200300 25 15 3268760 25 17 1081575 BINOMIAL_CDF_VALUES_TEST: BINOMIAL_CDF_VALUES returns values of the Binomial Cumulative Density Function. A B X CDF(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 BINOMIAL_PDF_VALUES_TEST: BINOMIAL_PDF_VALUES returns values of the Binomial Probability Density Function. A B X PDF(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 F(R)(X,Y) -2 1 0.5 0.02260327218569867 -1 1 0.5 0.15487295185841 0 1 0.5 0.4687428083352184 1 1 0.5 0.7452035868929476 2 1 0.5 0.8318608306874188 3 1 0.5 0.8410314261134202 -0.2 0.5 -0.9 0.1377019384919464 -0.2 0.5 -0.8 0.162174950173903 -0.2 0.5 -0.7 0.1827411243233119 -0.2 0.5 -0.6 0.2010067421506235 -0.2 0.5 -0.5 0.217775115526529 -0.2 0.5 -0.4 0.2335088436446962 -0.2 0.5 -0.3 0.2485057781834286 -0.2 0.5 -0.2 0.2629747825154868 -0.2 0.5 -0.1 0.2770729823404738 -0.2 0.5 0 0.2909261168683812 -0.2 0.5 0.1 0.3046406378726738 -0.2 0.5 0.2 0.3183113449213638 -0.2 0.5 0.3 0.3320262544108028 -0.2 0.5 0.4 0.3458686754647614 -0.2 0.5 0.5 0.3599150462310668 -0.2 0.5 0.6 0.3742210899871168 -0.2 0.5 0.7 0.388770640528232 -0.2 0.5 0.8 0.4032765198361344 -0.2 0.5 0.9 0.4162100291953678 1 0.5 0.673 0.6508271498838664 2 1 0.5 0.8318608306874188 0 0 -1 0 0 0 -0.5 0.166666666653997 0 0 0 0.25 0 0 0.5 0.3333333333328906 0 0 1 0.5 1 1 0.5 0.7452035868929476 1 -1 0.5 0.15487295185841 -1 1 0.5 0.15487295185841 -1 -1 0.5 0.06251409470431653 1 1 0.5 0.7452035868929476 1 -1 0.5 0.15487295185841 -1 1 0.5 0.15487295185841 -1 -1 0.5 0.06251409470431653 0.7071067811865475 0.7071067811865475 0.5 0.6337020457912916 CATALAN_VALUES_TEST: CATALAN_VALUES returns values of the Catalan numbers. N C(N) 0 1 1 1 2 2 3 5 4 14 5 42 6 132 7 429 8 1430 9 4862 10 16796 CAUCHY_CDF_VALUES_TEST: CAUCHY_CDF_VALUES 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 CBRT_VALUES_TEST: 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 CHEBY_T_POLY_VALUES_TEST: CHEBY_T_POLY_VALUES returns values of the Chebyshev T polynomials. N X T(N)(X) -1 0.8 0 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 CHEBY_T01_POLY_VALUES_TEST: CHEBY_T01_POLY_VALUES returns values of the shifted Chebyshev T polynomials. N X T01(N)(X) -1 0.85 0 0 0.85 1 1 0.85 0.7 2 0.85 -0.02 3 0.85 -0.728 4 0.85 -0.9992 5 0.85 -0.67088 6 0.85 0.059968 7 0.85 0.7548352 8 0.85 0.99680128 9 0.85 0.640686592 10 0.85 -0.0998400512 11 0.85 -0.7804626636799999 12 0.85 -0.992807677952 7 0 -1 7 0.1 0.2063872 7 0.2 -0.9784704 7 0.3 0.2580224 7 0.4 0.9870208 7 0.5 0 7 0.6 -0.9870208 7 0.7 -0.2580224 7 0.8 0.9784704 7 0.9 -0.2063872 7 1 1 CHEBY_U_POLY_VALUES_TEST: CHEBY_U_POLY_VALUES returns values of the Chebyshev U polynomials. N X U(N)(X) -1 0.8 0 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 -0.78683904 9 0.8 0.252071936 10 0.8 1.1901541376 11 0.8 1.65217468416 12 0.8 1.453325357056 CHEBY_U01_POLY_VALUES_TEST: CHEBY_U01_POLY_VALUES returns values of the shifted Chebyshev U polynomials. N X U01(N)(X) -1 0.85 0 0 0.85 1 1 0.85 1.4 2 0.85 0.96 3 0.85 -0.056 4 0.85 -1.0384 5 0.85 -1.39776 6 0.85 -0.9184639999999999 7 0.85 0.1119104 8 0.85 1.07513856 9 0.85 1.393283584 10 0.85 0.8754584576 11 0.85 -0.16764174336 12 0.85 -1.110156898304 7 0 -8 7 0.1 1.5110144 7 0.2 -1.1332608 7 0.3 -0.1636352 7 0.4 1.0198016 7 0.5 0 7 0.6 -1.0198016 7 0.7 0.1636352 7 0.8 1.1332608 7 0.9 -1.5110144 7 1 8 CHEBY_V_POLY_VALUES_TEST: CHEBY_V_POLY_VALUES returns values of the Chebyshev V polynomials. N X V(N)(X) -1 0.8 0 0 0.8 1 1 0.8 0.6 2 0.8 -0.04 3 0.8 -0.664 4 0.8 -1.0224 5 0.8 -0.97184 6 0.8 -0.532544 7 0.8 0.1197696 8 0.8 0.72417536 9 0.8 1.038910976 10 0.8 0.9380822016 11 0.8 0.46202054656 12 0.8 -0.198849327104 CHEBY_V01_POLY_VALUES_TEST: CHEBY_V01_POLY_VALUES returns values of the shifted Chebyshev V polynomials. N X V01(N)(X) -1 0.85 0 0 0.85 1 1 0.85 0.4 2 0.85 -0.44 3 0.85 -1.016 4 0.85 -0.9824000000000001 5 0.85 -0.35936 6 0.85 0.479296 7 0.85 1.0303744 8 0.85 0.96322816 9 0.85 0.318145024 10 0.85 -0.5178251264 11 0.85 -1.04310020096 12 0.85 -0.942515154944 7 0 -15 7 0.1 3.1417984 7 0.2 -1.3912448 7 0.3 -1.2177792 7 0.4 1.1837056 7 0.5 1 7 0.6 -0.8558976 7 0.7 -0.8905088 7 0.8 0.8752768 7 0.9 0.1197696 7 1 1 CHEBY_W_POLY_VALUES_TEST: CHEBY_W_POLY_VALUES returns values of the Chebyshev W polynomials. N X W(N)(X) -1 0.8 0 0 0.8 1 1 0.8 2.6 2 0.8 3.16 3 0.8 2.456 4 0.8 0.7696 5 0.8 -1.22464 6 0.8 -2.729024 7 0.8 -3.1417984 8 0.8 -2.29785344 9 0.8 -0.534767104 10 0.8 1.4422260736 11 0.8 2.84232882176 12 0.8 3.105500041216 CHEBY_W01_POLY_VALUES_TEST: CHEBY_W01_POLY_VALUES returns values of the shifted Chebyshev W polynomials. N X W01(N)(X) -1 0.85 0 0 0.85 1 1 0.85 2.4 2 0.85 2.36 3 0.85 0.904 4 0.85 -1.0944 5 0.85 -2.43616 6 0.85 -2.316224 7 0.85 -0.8065536 8 0.85 1.18704896 9 0.85 2.468422144 10 0.85 2.2687420416 11 0.85 0.70781671424 12 0.85 -1.277798641664 7 0 -1 7 0.1 -0.1197696 7 0.2 -0.8752768 7 0.3 0.8905088 7 0.4 0.8558976 7 0.5 -1 7 0.6 -1.1837056 7 0.7 1.2177792 7 0.8 1.3912448 7 0.9 -3.1417984 7 1 15 CHI_VALUES_TEST: 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 CHI_SQUARE_CDF_VALUES_TEST: 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 CHI_SQUARE_PDF_VALUES_TEST: CHI_SQUARE_PDF_VALUES returns values of the Chi-Squared Probability Density Function. DF X PDF(X) 1 0.01 3.969525474770117 2 0.01 0.4975062395963412 1 0.02 2.792879016972342 2 0.02 0.4950249168745841 1 0.4 0.5164415474672784 2 0.4 0.4093653765389909 3 0.4 0.2065766189869113 4 0.4 0.08187307530779819 1 1 0.2419707245191434 2 1 0.3032653298563167 3 1 0.2419707245191434 4 1 0.1516326649281584 5 1 0.08065690817304777 3 2 0.2075537487102974 3 3 0.1541803298037693 3 4 0.1079819330263761 3 5 0.07322491280963248 3 6 0.04865217332964145 10 1 0.0007897534631674914 10 2 0.00766415502440505 10 3 0.02353325907815472 CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST: CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral Chi-Squared Cumulative Density Function. X LAMBDA DF CDF 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 CI_VALUES_TEST: 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 CIN_VALUES_TEST: 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 CINH_VALUES_TEST: CINH_VALUES stores values of the Hyperbolic Cosine Integral function CINH(X). X CINH(X) 0 0 0.5 0.06315467070191882 0.6 0.09136085223843649 0.7 0.1250284547325902 0.8 0.1643278712460683 0.9 0.2094587379417273 1 0.2606512760786754 1.2 0.3823047024751071 1.4 0.531806174266898 1.6 0.7122865135136963 1.8 0.9275748842583805 2 1.182304077185436 2.5 2.030919091578478 3 3.284564141195967 3.5 5.129213294250493 4 7.850037532801762 4.5 11.88451858691463 CLAUSEN_VALUES_TEST: 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 CLEBSCH_GORDAN_VALUES_TEST: 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 COLLATZ_COUNT_VALUES_TEST: COLLATZ_COUNT_VALUES returns values of the length of the Collatz sequence that starts at N. N COLLATZ_COUNT(N) 1 1 2 2 3 8 4 3 5 6 6 9 7 17 8 4 9 20 10 7 27 112 50 25 100 26 200 27 300 17 400 28 500 111 600 18 700 83 800 29 COS_VALUES_TEST: COS_VALUES stores values of the cosine function. X FX 0 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 COS_DEGREE_VALUES_TEST: COS_DEGREE_VALUES stores values of the cosine function. X FX -5 0.9961946980917455 0 1 1 0.9998476951563913 2 0.9993908270190958 3 0.9986295347545738 4 0.9975640502598242 5 0.9961946980917455 10 0.984807753012208 15 0.9659258262890683 30 0.8660254037844386 45 0.7071067811865476 60 0.5 75 0.2588190451025207 85 0.08715574274765818 86 0.0697564737441253 87 0.05233595624294383 88 0.03489949670250097 89 0.01745240643728351 90 0 91 -0.01745240643728351 105 -0.2588190451025207 180 -1 COS_POWER_INT_VALUES_TEST: COS_POWER_INT_VALUES returns values of the integral of the N-th power of the cosine function. A B N FX 0 3.141592653589793 0 3.141592653589793 0 3.141592653589793 1 0 0 3.141592653589793 2 1.570796326794897 0 3.141592653589793 3 0 0 3.141592653589793 4 1.178097245096172 0 3.141592653589793 5 0 0 3.141592653589793 6 0.9817477042468103 0 3.141592653589793 7 0 0 3.141592653589793 8 0.8590292412159591 0 3.141592653589793 9 0 0 3.141592653589793 10 0.7731263170943632 COSH_VALUES_TEST: 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 COT_VALUES_TEST: COT_VALUES stores values of the cotangent function. X FX 0.08333333333333333 11.97220935362866 0.2617993877991495 3.732050807568877 0.5 1.830487721712452 0.5235987755982989 1.732050807568877 0.7853981633974483 1 1 0.6420926159343308 1.047197551196598 0.5773502691896257 1.308996938995747 0.2679491924311227 1.570796326794897 0 1.439896632895322 0.1316524975873959 1.505346479845109 0.06554346281523823 2 -0.4576575543602858 3 -7.015252551434534 4 0.8636911544506166 5 -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 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 DATENUM_VALUES_TEST: DATENUM_VALUES returns values of the MATLAB datenum for a given Y/M/D date. Y M D DATENUM 0 1 1 1 1 1 1 367 100 1 1 36526 1000 1 1 365244 1939 8 17 708434 1944 9 9 710284 1952 3 10 713023 1966 5 12 718199 1980 1 6 723186 1996 2 25 729080 2000 1 1 730486 DAWSON_VALUES_TEST: DAWSON_VALUES stores values of Dawson's integral function. X DAWSON(X) 0 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 DEBYE1_VALUES_TEST: 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 DEBYE2_VALUES_TEST: 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 DEBYE3_VALUES_TEST: 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 DEBYE4_VALUES_TEST: 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 DEDEKIND_SUM_VALUES_TEST: DEDEKIND_SUM_VALUES stores values of the Dedekind sum (N/D) = Dedekind_Sum(P,Q). P Q N D 1 1 0 1 1 2 0 1 1 3 1 18 1 4 1 8 1 5 1 5 1 6 5 18 1 7 5 14 1 8 7 16 1 9 14 27 1 10 3 5 1 11 15 22 1 12 55 72 1 13 11 13 1 14 13 14 1 15 91 90 1 16 35 32 1 17 20 17 1 18 34 27 1 19 51 38 1 20 57 40 2 1 0 1 2 3 -1 18 2 5 0 1 2 7 1 14 2 9 4 27 2 11 5 22 2 13 4 13 2 15 7 18 2 17 8 17 2 19 21 38 3 1 0 1 3 2 0 1 3 4 -1 8 3 5 0 1 3 7 -1 14 3 8 1 16 3 10 0 1 3 11 3 22 3 13 1 13 3 14 3 14 3 16 5 32 3 17 5 17 3 19 9 38 3 20 3 8 4 1 0 1 4 3 1 18 4 5 -1 5 4 7 1 14 4 9 -4 27 4 11 3 22 4 13 -1 13 4 15 19 90 4 17 0 1 4 19 11 38 5 1 0 1 5 2 0 1 5 3 -1 18 5 4 1 8 5 6 -5 18 5 7 -1 14 5 8 -1 16 5 9 4 27 5 11 -5 22 5 12 -1 72 5 13 0 1 5 14 3 14 5 16 -5 32 5 17 1 17 5 18 2 27 5 19 11 38 6 1 0 1 6 5 1 5 6 7 -5 14 6 11 5 22 6 13 -4 13 6 17 5 17 6 19 -9 38 7 1 0 1 7 2 0 1 7 3 1 18 7 4 -1 8 7 5 0 1 7 6 5 18 7 8 -7 16 7 9 -4 27 7 10 0 1 7 11 -3 22 7 12 1 72 7 13 4 13 7 15 -7 18 7 16 -3 32 7 17 1 17 7 18 -2 27 7 19 3 38 7 20 3 8 DIELECTRIC_VALUES_TEST: DIELECTRIC_VALUES stores values of the dielectric function. T P EPS(T,P) 0 100 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 DILOGARITHM_VALUES_TEST: 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 E1_VALUES_TEST: 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 EASTER_GREGORIAN_VALUES_TEST: EASTER_GREGORIAN_VALUES returns 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 returns values of the date of Easter in the Julian calendar. D M Y 27 4 1997 19 4 1998 11 4 1999 30 4 2000 15 4 2001 5 5 2002 27 4 2003 11 4 2004 1 5 2005 23 4 2006 EI_VALUES_TEST: EI_VALUES stores values of the exponential integral function EI(X). X EI(X) 0.5 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 ELLIPTIC_EA_VALUES_TEST: ELLIPTIC_EA_VALUES stores values of the complete elliptic integral of the second kind, with parameter angle A in degrees. A E(A) 0 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 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 1.570796326794897 0.2236068 1.550973351780472 0.31622777 1.530757636897763 0.38729833 1.510121832092819 0.4472136 1.489035058095853 0.5 1.467462209339427 0.54772256 1.445363064412665 0.59160798 1.422691133490879 0.63245553 1.399392138897432 0.67082039 1.375401971871116 0.70710678 1.350643881047676 0.74161985 1.32502449795823 0.77459667 1.298428035046913 0.80622577 1.270707479650149 0.83666003 1.241670567945823 0.8660254 1.211056027568459 0.89442719 1.178489924327839 0.92195445 1.143395791883166 0.9486833 1.104774732704073 0.97467943 1.060473727766278 1 1 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 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 ELLIPTIC_FA_VALUES_TEST: ELLIPTIC_FA_VALUES stores values of the complete elliptic integral of the first kind, with parameter angle A in degrees. A F(A) 0 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 ELLIPTIC_FK_VALUES_TEST: ELLIPTIC_FK_VALUES stores values of the complete elliptic integral of the first kind, with parameter K. K F(K) 0 1.570796326794897 0.2236068 1.591003453790792 0.31622777 1.612441348720219 0.38729833 1.63525673226458 0.4472136 1.659623598610528 0.5 1.685750354812596 0.54772256 1.713889448178791 0.59160798 1.744350597225613 0.63245553 1.777519371491253 0.67082039 1.813883936816983 0.70710678 1.854074677301372 0.74161985 1.898924910271554 0.77459667 1.949567749806026 0.80622577 2.007598398424376 0.83666003 2.075363135292469 0.8660254 2.156515647499643 0.89442719 2.257205326820854 0.92195445 2.38901648632558 0.9486833 2.578092113348173 0.97467943 2.908337248444552 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 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 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 123.082 0.3384181367348019 1.30299 11.2693 1.292924624509506 0.652363 -94.8881 0.6074183768796306 0.404602 -99.7141 0.3939726730783567 0.0688464 57.0588 0.06880814097089803 0.0969609 -19.7136 0.0969436473376824 0.63037 56.3123 0.6025937791452033 1.25238 -91.5561 0.9500549494837583 1.4098 -27.0065 1.342783372140486 0.148511 -169.229 0.1484915631401388 1.34947 61.9686 1.085432887050926 0.193371 -158.732 0.1932136916085597 0.408883 105.088 0.3983689593057807 0.178543 -48.9588 0.1780054133336934 1.29259 -42.5857 1.164525270273536 1.0871 11.656 1.080167047541845 1.35279 -8.39811 1.346684963830312 1.43253 17.6936 1.402100272685504 0.296809 73.8803 0.2928091845544553 0.623588 -69.8249 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 2.71295 -0.2852345328295404 1.30299 0.127952 -1.298690225567921 0.652363 -1.42944 -0.5508100202571943 0.404602 -1.98166 -0.3575401358115371 0.0688464 3.8948 -0.06801307805507453 0.0969609 -1.04249 -0.09679584980231837 0.63037 0.864114 -0.6003112504412838 1.25238 -1.04906 -0.8996717721794724 1.4098 -0.302406 -1.380715261453875 0.148511 -6.57429 -0.1191644625202453 1.34947 0.69874 -1.196994838171557 0.193371 -5.12559 -0.1536260979667945 0.408883 2.07495 -0.3546768920544152 0.178543 -1.67089 -0.1758756066650882 1.29259 -0.48436 -1.229819109410569 1.0871 0.139306 -1.08381066114337 1.35279 -0.0946527 -1.35023378157378 1.43253 0.197721 -1.419775884709218 0.296809 1.78816 -0.2824895528020034 0.623588 -1.07778 -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 8.45069 0.2732317284159052 1.30299 0.603988 1.124749725099781 0.652363 0.179413 0.6446601913679151 0.404602 0.709569 0.3968902354370061 0.0688464 133.964 0.06063960799944668 0.0969609 47.9662 0.08909411577948728 0.63037 2.17207 0.532402014802015 1.25238 0.00203813 1.251888640660265 1.4098 0.360004 1.28897116191626 0.148511 0.621954 0.1481718153599732 1.34947 0.883422 1.038090185639913 0.193371 0.203429 0.1931275771541276 0.408883 5.77253 0.3304419611986801 0.178543 11.1485 0.167394796063963 1.29259 0.288924 1.214501175324736 1.0871 0.716662 0.9516560179840655 1.35279 0.476062 1.203682959526176 1.43253 0.609495 1.206426326185419 0.296809 8.90228 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 123.082 0.3478806460316299 1.30299 11.2693 1.313180577009584 0.652363 -94.8881 0.7037956689264326 0.404602 -99.7141 0.4157626844675118 0.0688464 57.0588 0.06888475483285136 0.0969609 -19.7136 0.09697816754845832 0.63037 56.3123 0.6605394722518515 1.25238 -91.5561 1.82758346036751 1.4098 -27.0065 1.482258783392487 0.148511 -169.229 0.1485295339221232 1.34947 61.9686 1.753800062701494 0.193371 -158.732 0.193528896465351 0.408883 105.088 0.4199100508706138 0.178543 -48.9588 0.1790836490491233 1.29259 -42.5857 1.446048832279763 1.0871 11.656 1.094097652100984 1.35279 -8.39811 1.358947908427035 1.43253 17.6936 1.46400078231538 0.296809 73.8803 0.3009092014525799 0.623588 -69.8249 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 2.71295 0.4340870330108736 1.30299 0.127952 1.307312511398114 0.652363 -1.42944 0.8005154258533936 0.404602 -1.98166 0.4656721451084328 0.0688464 3.8948 0.06969849613441773 0.0969609 -1.04249 0.09712646708750489 0.63037 0.864114 0.6632598061016007 1.25238 -1.04906 2.2308677858579 1.4098 -0.302406 1.439846282888019 0.148511 -6.57429 0.2043389243773096 1.34947 0.69874 1.537183574881771 0.193371 -5.12559 0.2749229901565622 0.408883 2.07495 0.4828388342828284 0.178543 -1.67089 0.1812848567886627 1.29259 -0.48436 1.360729522341841 1.0871 0.139306 1.09039680912027 1.35279 -0.0946527 1.355363051581808 1.43253 0.197721 1.445462819732441 0.296809 1.78816 0.3125355489354676 0.623588 -1.07778 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 8.45069 0.4804314075855023 1.30299 0.603988 1.535634981092025 0.652363 0.179413 0.6602285297476601 0.404602 0.709569 0.4125884303785135 0.0688464 133.964 0.07964566007155376 0.0969609 47.9662 0.1062834070535258 0.63037 2.17207 0.7733990864393913 1.25238 0.00203813 1.252862499892228 1.4098 0.360004 1.549988686611532 0.148511 0.621954 0.1488506735822822 1.34947 0.883422 1.892229900799662 0.193371 0.203429 0.1936153327753556 0.408883 5.77253 0.5481932935424454 0.178543 11.1485 0.1911795073571756 1.29259 0.288924 1.379225069349756 1.0871 0.716662 1.261282453331402 1.35279 0.476062 1.535239838525378 1.43253 0.609495 1.739782418156071 0.296809 8.90228 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 8.06468 88.8782 0.7099335174334724 0.882309 -0.284059 -86.5521 0.9601963779142505 0.404602 -5.03402 -116.62 0.3362852532098376 0.995831 -1.24461 -9.74288 0.7785343427543768 0.63037 1.46598 65.7348 0.857889755214478 0.00288771 95338.1 -115.039 0.004630772344931844 0.148511 -44.4313 124.942 0.1173842687902911 1.3208 -0.802937 -89.787 1.505788070660267 0.408883 5.21888 -98.4267 0.7213264194624553 0.552337 2.34582 -53.7494 0.8073261799642218 1.0871 0.157358 68.2805 1.402853811110838 0.712818 1.92659 20.8217 1.259245331474513 0.296809 6.11398 -29.1042 0.3779079263971614 0.291091 1.80571 -37.8018 0.3088493910496766 0.969503 -0.407285 -55.8117 0.9782829177005183 1.12229 -0.94164 -37.6659 0.9430491574504173 1.29591 0.700966 -80.0941 3.320796277384155 1.11649 -1.01983 52.2381 0.9730988737054799 1.17072 -0.45108 74.3095 1.301988094953789 1.19936 0.602882 -17.2292 1.64558360445259 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 8.06468 1.95904 0.7982975462595892 0.882309 -0.284059 -1.12374 1.024022134726036 0.404602 -5.03402 -2.31763 0.40158120852642 0.995831 -1.24461 -0.120258 0.7772649487439858 0.63037 1.46598 1.0087 0.8737159913132074 0.00288771 95338.1 -103.368 0.004733334297691273 0.148511 -44.4313 4.8538 0.1280656893638068 1.3208 -0.802937 -1.01658 1.594376037512564 0.408883 5.21888 -1.94341 0.8521145133671923 0.552337 2.34582 -0.887659 0.8154325229803082 1.0871 0.157358 0.816049 1.31594514075427 0.712818 1.92659 0.299455 1.25394623148424 0.296809 6.11398 -0.704423 0.3796503567258643 0.291091 1.80571 -0.926652 0.3111034454739552 0.969503 -0.407285 -0.696261 0.9442477901112342 1.12229 -0.94164 -0.445393 0.9153111661980959 1.29591 0.700966 -0.910458 2.842080644328393 1.11649 -1.01983 0.61875 0.9263253777034376 1.17072 -0.45108 0.867231 1.212396018757624 1.19936 0.602882 -0.199677 1.628083572710471 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 8.06468 7.33012 1.0469349800785 0.882309 -0.284059 0.110881 0.842114448140669 0.404602 -5.03402 0.282836 0.3321642201520043 0.995831 -1.24461 0.6383 0.8483033529960849 0.63037 1.46598 2.29472 1.055753817656772 0.00288771 95338.1 42062.6 0.005108896144265593 0.148511 -44.4313 39.2394 0.1426848042785896 1.3208 -0.802937 0.00800215 1.031350958206424 0.408883 5.21888 0.719058 0.7131013701418496 0.552337 2.34582 0.970377 0.8268044665355507 1.0871 0.157358 1.09888 1.57632867896015 0.712818 1.92659 1.39807 1.542817120857211 0.296809 6.11398 4.64102 0.4144629799126912 0.291091 1.80571 4.45597 0.3313231611366746 0.969503 -0.407285 0.313145 0.9195822851915201 1.12229 -0.94164 0.368644 0.9422320754002217 1.29591 0.700966 0.0667821 2.036599002815859 1.11649 -1.01983 0.963554 1.076799231499882 1.17072 -0.45108 1.06021 1.416084462957852 1.19936 0.602882 0.468716 1.824124922310891 ELLIPTIC_PIA_VALUES_TEST: ELLIPTIC_PIA_VALUES stores values of the complete elliptic integral of the third kind, with parameter angle A in degrees. N A Pi(N,A) -10 30 0.4892245275965397 -10 45 0.5106765677902629 -10 60 0.5460409271920561 -10 77.079034 0.6237325893535237 -3 30 0.823045542660675 -3 45 0.8760028274011437 -3 60 0.9660073560143946 -3 77.079034 1.171952391481798 -1 30 1.177446843000566 -1 45 1.273127366749682 -1 60 1.440034318657551 -1 77.079034 1.836472172302591 0 30 1.685750354812596 0 45 1.854074677301372 0 60 2.156515647499643 0 77.079034 2.908337248444552 0.5 30 2.413671504201195 0.5 45 2.701287762095351 0.5 60 3.234773471249465 0.5 77.079034 4.633308147279891 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 0.5 0.4892245275965397 -10 0.70710678 0.5106765677902629 -10 0.8660254 0.5460409271920561 -10 0.97467943 0.6237325893535237 -3 0.5 0.823045542660675 -3 0.70710678 0.8760028274011437 -3 0.8660254 0.9660073560143946 -3 0.97467943 1.171952391481798 -1 0.5 1.177446843000566 -1 0.70710678 1.273127366749682 -1 0.8660254 1.440034318657551 -1 0.97467943 1.836472172302591 0 0.5 1.685750354812596 0 0.70710678 1.854074677301372 0 0.8660254 2.156515647499643 0 0.97467943 2.908337248444552 0.5 0.5 2.413671504201195 0.5 0.70710678 2.701287762095351 0.5 0.8660254 3.234773471249465 0.5 0.97467943 4.633308147279891 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 0.25 0.4892245275965397 -10 0.5 0.5106765677902629 -10 0.75 0.5460409271920561 -10 0.95 0.6237325893535237 -3 0.25 0.823045542660675 -3 0.5 0.8760028274011437 -3 0.75 0.9660073560143946 -3 0.95 1.171952391481798 -1 0.25 1.177446843000566 -1 0.5 1.273127366749682 -1 0.75 1.440034318657551 -1 0.95 1.836472172302591 0 0.25 1.685750354812596 0 0.5 1.854074677301372 0 0.75 2.156515647499643 0 0.95 2.908337248444552 0.5 0.25 2.413671504201195 0.5 0.5 2.701287762095351 0.5 0.75 3.234773471249465 0.5 0.95 4.633308147279891 ERF_VALUES_TEST: 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 ERFC_VALUES_TEST: 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 EULER_NUMBER_VALUES_TEST: EULER_NUMBER_VALUES returns values of the Euler numbers. N EULER_NUMBER(N) 0 1 1 0 2 -1 4 5 6 -61 8 1385 10 -50521 12 2702765 EULER_POLY_VALUES_TEST: EULER_POLY_VALUES returns values of the Euler 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 EXP_VALUES_TEST: 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 EXP3_INT_VALUES_TEST: 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 EXPONENTIAL_01_PDF_VALUES_TEST: EXPONENTIAL_01_PDF_VALUES stores values of the standard exponential Probability Density Function. X PDF(X) 0.7013006334030669 0.4959398481993681 4.759746670799113 0.00856777959135697 4.062300786629853 0.01720937842266235 2.589324935217918 0.07507070056996956 1.784188948117787 0.1679332083261492 -0.1363469579618277 0 0.9166778581012469 0.399845179478639 0.1047623644285883 0.9005384971416223 -0.2589405122149109 0 2.986811417663269 0.05044803826563792 EXPONENTIAL_CDF_VALUES_TEST: EXPONENTIAL_CDF_VALUES stores values of the exponential CDF. LAMBDA X FX 0.5 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 EXPONENTIAL_PDF_VALUES_TEST: EXPONENTIAL_PDF_VALUES stores values of the exponential PDF. LAMBDA X FX 1.0920915 9.5588075 0.0001446999730194618 4.1475462 5.573124 0.06289850821824726 2.0765354 0.56779922 0.3663607831924032 1.287889 1.0105636 0.3542787877169571 0.21914499 6.3030537 1.472582451176006e-12 0.30863615 4.4403435 1.829637907028298e-06 2.0065314 7.5222022 0.01173398427218792 3.9864348 -0.081432451 0 4.4875203 3.4425986 0.1034724689882351 0.47272375 0.037530605 1.95394780436833 EXTREME_VALUES_CDF_VALUES_TEST: 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 F_CDF_VALUES_TEST: 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 F_NONCENTRAL_CDF_VALUES_TEST: 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 FRESNEL_COS_VALUES_TEST: 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 FRESNEL_SIN_VALUES_TEST: 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 FROBENIUS_NUMBER_DATA_VALUES_TEST: FROBENIUS_NUMBER_DATA_VALUES returns the corresponding coin denominations. Order = 2 2 5 Frobenius number = 3 Order = 2 3 17 Frobenius number = 31 Order = 2 4 19 Frobenius number = 53 Order = 2 5 13 Frobenius number = 47 Order = 2 12 11 Frobenius number = 109 Order = 2 99 100 Frobenius number = 9701 Order = 3 6 9 20 Frobenius number = 43 Order = 3 5 17 23 Frobenius number = 41 Order = 3 137 251 256 Frobenius number = 4948 Order = 4 31 41 47 61 Frobenius number = 240 Order = 4 271 277 281 283 Frobenius number = 13022 Order = 5 10 18 26 33 35 Frobenius number = 67 Order = 5 34 37 38 40 43 Frobenius number = 175 Order = 5 12223 12224 36674 61119 85569 Frobenius number = 89643481 Order = 6 1000 1476 3764 4864 4871 7773 Frobenius number = 47350 Order = 6 12228 36679 36682 46908 61139 73365 Frobenius number = 89716838 Order = 6 12137 36405 24269 36407 84545 60683 Frobenius number = 58925134 Order = 7 13211 13212 39638 66060 52864 79268 92482 Frobenius number = 104723595 Order = 8 13429 26850 26855 40280 40281 53711 53714 67141 Frobenius number = 45094583 FROBENIUS_NUMBER_ORDER_VALUES_TEST: FROBENIUS_NUMBER_ORDER_VALUES returns the order for a Frobenius problem; 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) -0.5 -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 GAMMA_01_PDF_VALUES_TEST: GAMMA_01_PDF_VALUES stores values of the standard Gamma Probability Density Function. ALPHA X PDF(X) 1.092091484911879 9.541334553343761 9.260811963612823e-05 4.147546169663503 5.39780214905239 0.1260335478747823 2.076535407379806 0.1942467166183289 0.1363536772414351 1.287888961910225 0.6545463320909413 0.5114450139194701 0.2191449888955355 6.156639979175331 0.0001230139468263628 0.3086361453280091 4.220159083225351 0.001870342832511005 2.006531407488083 7.424071607424807 0.004476000451227789 3.986434770531281 -0.4806971028367454 0 4.487520304498656 3.18289954879574 0.2056668486524041 0.472723751058401 -0.3570226383736496 0 GAMMA_CDF_VALUES_TEST: 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 GAMMA_INC_VALUES_TEST: GAMMA_INC_VALUES stores values of the incomplete Gamma function. A X GAMMA_INC(A)(X) 0.1 0.03 2.49030283630057 0.1 0.3 0.8718369702247978 0.1 1.5 0.1079213896175866 0.5 0.075 1.238121685818417 0.5 0.75 0.3911298052193973 0.5 3.5 0.01444722098952533 1 0.1 0.9048374180359596 1 1 0.3678794411714423 1 5 0.006737946999085467 1.1 0.1 0.8827966752611692 1.1 1 0.3908330082003269 1.1 5 0.008051456628620992 2 0.15 0.9898141728888165 2 1.5 0.5578254003710746 2 7 0.00729505572443613 6 2.5 114.9574754165633 6 12 2.440923530031405 11 16 280854.6620274718 26 25 8.576480283455533e+24 41 45 2.085031346403364e+47 GAMMA_INC_P_VALUES_TEST: GAMMA_INC_P_VALUES stores values of the incomplete Gamma P function. A X F(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 GAMMA_INC_Q_VALUES_TEST: GAMMA_INC_Q_VALUES stores values of the incomplete Gamma Q function. A X F(X) 0.1 0.03 0.2617649467660649 0.1 0.3 0.09164201026996573 0.1 1.5 0.01134401663780527 0.5 0.075 0.6985353583033387 0.5 0.75 0.2206713619198468 0.5 3.5 0.0081509715935027 1 0.1 0.9048374180359596 1 1 0.3678794411714423 1 5 0.006737946999085467 1.1 0.1 0.9279402542394568 1.1 1 0.4108190381293515 1.1 5 0.008463184015447498 2 0.15 0.9898141728888165 2 1.5 0.5578254003710746 2 7 0.00729505572443613 6 2.5 0.9579789618046939 6 12 0.02034102941692837 11 16 0.07739601577035708 26 25 0.5529214200244148 41 45 0.2555450779281301 GAMMA_INC_TRICOMI_VALUES_TEST: GAMMA_INC_TRICOMI_VALUES stores values of the incomplete Tricomi Gamma function. A X F(X) 0.1 0.03 1.048292641463504 0.1 0.3 1.024577737369574 0.1 1.5 0.9493712443185374 0.5 0.075 1.100793230316492 0.5 0.75 0.8998911979655217 0.5 3.5 0.5301656062431039 1 0.1 0.9516258196404043 1 1 0.6321205588285577 1 5 0.1986524106001829 1.1 0.1 0.9071784510537487 1.1 1 0.5891809618706485 1.1 5 0.1688269752193589 2 0.15 0.4527034271637121 2 1.5 0.1965220442795224 2 7 0.02025928457705232 6 2.5 0.0001721181724479739 6 12 3.280858070850586e-07 11 16 5.24439647182159e-14 26 25 2.013462926183376e-37 41 45 1.230623887499875e-68 GAMMA_LOG_VALUES_TEST: 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 GAMMA_PDF_VALUES_TEST: GAMMA_PDF_VALUES stores values of a Gamma Probability Density Function. BETA ALPHA X PDF(X) 1.092091484911879 4.781587882544648 4.942957250382744 0.1672017697220646 2.808477213834471 2.076535407379806 0.2099361564793942 0.8522122814089312 1.287888961910225 0.549783967662353 0.07173978623046406 2.122272611165834 3.169828561512062 0.3086361453280091 2.587141553904492 6.993771842317114e-05 2.006531407488083 3.773367432107051 4.743179115458788 0.01679379733182281 0.009191855792026001 4.487520304498656 1.974664495479389 6.687464259463117e-10 0.472723751058401 0.06808445791730976 5.126400502735112 0.001295436045931343 4.204237253278341 0.6155195788227712 -0.1534233427414219 0 1.301514988836825 4.562418534907164 0.5047170879434957 0.01189893036865762 1.758143299519481 4.114436583429598 1.456220075613112 0.3658836103539945 GEGENBAUER_POLY_VALUES_TEST: 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 GEOMETRIC_CDF_VALUES_TEST: 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 GOODWIN_VALUES_TEST: 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 GUD_VALUES_TEST: 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 HERMITE_FUNCTION_VALUES_TEST HERMITE_FUNCTION_VALUES stores values of the Hermite function. N X Hf(N,X) 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 physicist's 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 0 5 0.5 41 5 1 -8 5 3 3816 5 10 3041200 HERMITE_POLY_PROB_VALUES_TEST HERMITE_POLY_PROB_VALUES stores values of the probabilist's Hermite polynomials. N X He(N,X) 0 5 1 1 5 5 2 5 24 3 5 110 4 5 478 5 5 1950 6 5 7360 7 5 25100 8 5 73980 9 5 169100 10 5 179680 11 5 -792600 12 5 -5939480 5 0 0 5 0.5 6.28125 5 1 6 5 3 18 5 10 90150 HYPER_1F1_VALUES_TEST: HYPER_1F1_VALUES stores values of the hypergeometric function 1F1. A B X Hyper_1F1(A,B,X) -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 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 HYPERGEOMETRIC_CDF_VALUES_TEST: 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 HYPERGEOMETRIC_PDF_VALUES_TEST: 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 HYPERGEOMETRIC_U_VALUES_TEST: HYPERGEOMETRIC_U_VALUES stores values of the hypergeometric function U. A B X HyperU(A,B,X) -2.5 3.3 0.25 -68.69362872807861 -0.5 1.1 0.25 -0.002971055137476107 0.5 1.1 0.25 1.50086317421778 2.5 3.3 0.25 20.6146882442006 -2.5 3.3 1.55 7.456381546930555 -0.5 1.1 1.55 1.015579376774929 0.5 1.1 1.55 0.7344653893662267 2.5 3.3 1.55 0.280464049418794 -2.5 3.3 2.85 3.450815374144655 -0.5 1.1 2.85 1.515663736875306 0.5 1.1 2.85 0.56042118587935 2.5 3.3 2.85 0.06489714773513422 0.825 6.7 0.25 223432.0235697746 1.1 6.7 0.25 263079.2598074081 1.65 6.7 0.25 269802.9031935128 3.3 6.7 0.25 82809.31133560656 0.825 6.7 1.55 26.46568478313185 1.1 6.7 1.55 28.09350617251606 1.65 6.7 1.55 23.88916462451887 3.3 6.7 1.55 4.533884785707039 0.825 6.7 2.85 3.022446936269484 1.1 6.7 2.85 2.804065091371336 1.65 6.7 2.85 1.926257811148017 3.3 6.7 2.85 0.2302051811586091 I0ML0_VALUES_TEST: 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 I1ML1_VALUES_TEST: 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 I4_FACTORIAL_TEST: I4_FACTORIAL_VALUES returns values of the 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 I4_FACTORIAL2_TEST: I4_FACTORIAL2_VALUES return;s values of the double factorial function. N DoubleFactorial(N) 0 1 1 1 2 2 3 3 4 8 5 15 6 48 7 105 8 384 9 945 10 3840 11 10395 12 46080 13 135135 14 645120 15 2027025 I4_FALL_VALUES_TEST: I4_FALL_VALUES returns some exact values of the integer falling factorial function: M N I4_FALL(M,N) 5 0 1 5 1 5 5 2 20 5 3 60 5 4 120 5 5 120 5 6 0 50 0 1 10 1 10 4000 1 4000 10 2 90 18 3 4896 4 4 24 98 3 912576 1 7 0 I4_RISE_VALUES_TEST: I4_RISE_VALUES returns some exact values of the integer rising factorial function: M N I4_RISE(M,N) 5 0 1 5 1 5 5 2 30 5 3 210 5 4 1680 5 5 15120 5 6 151200 50 0 1 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 of a real number. X INT(X) -2.01 -2 -1.99 -1 -1.5 -1 -1.1 -1 -1.01 -1 -1 -1 -0.99 0 -0.9 0 -0.51 0 -0.5 0 -0.49 0 -0.01 0 0 0 0.01 0 0.49 0 0.5 0 0.51 0 0.9 0 0.99 0 1 1 1.01 1 1.1 1 1.5 1 1.99 1 2.01 2 INVERSE_CHI_SQUARE_PDF_VALUES_TEST: INVERSE_CHI_SQUARE_PDF_VALUES returns values of the inverse Chi-Square Probability Density Function. DF X PDF 1 0.1 0.08500366602520341 2 0.1 0.3368973499542734 1 0.2 0.3661245640481622 2 0.2 1.026062482798735 1 0.4 0.4518059816704532 2 0.4 0.8953274901880941 3 0.4 1.129514954176133 4 0.4 1.119159362735118 1 1 0.2419707245191433 2 1 0.3032653298563167 3 1 0.2419707245191433 4 1 0.1516326649281584 5 1 0.08065690817304778 3 2 0.0549239111834653 3 3 0.02166329508030457 3 4 0.01100204146138436 3 5 0.006457369034861447 3 6 0.004162370481945731 10 1 0.0007897534631674914 10 2 1.584474249412852e-05 10 3 1.511920090468204e-06 INVERSE_GAMMA_PDF_VALUES_TEST: INVERSE_GAMMA_PDF_VALUES returns values of the inverse gamma Probability Density Function. ALPHA BETA X PDF 1 0.5 1 0.3032653298563167 1 0.5 2 0.09735009788392561 1 0.5 3 0.047026762493923 1 0.5 4 0.02757802820576861 1 2 2 0.1839397205857212 1 3 2 0.1673476201113224 1 4 2 0.1353352832366127 1 5 2 0.1026062482798735 2 2 3 0.07606179541223586 3 2 3 0.02535393180407862 4 2 3 0.005634207067573026 5 2 3 0.0009390345112621711 JACOBI_CN_VALUES_TEST: JACOBI_CN_VALUES returns values of the Jacobi elliptic CN function. U M CN(U,M) 0.1 0 0.9950041652780258 0.2 0 0.9800665778412416 0.5 0 0.8775825618903726 1 0 0.5403023058681397 2 0 -0.4161468365471424 0.1 0.5 0.9950124626090582 0.2 0.5 0.9801976276784098 0.5 0.5 0.8822663948904403 1 0.5 0.5959765676721407 2 0.5 -0.1031836155277618 0.1 1 0.9950207489532265 0.2 1 0.9803279976447253 0.5 1 0.8868188839700739 1 1 0.6480542736638853 2 1 0.2658022288340797 4 1 0.03661899347368653 -0.2 1 0.9803279976447253 -0.5 1 0.8868188839700739 -1 1 0.6480542736638853 -2 1 0.2658022288340797 JACOBI_DN_VALUES_TEST: JACOBI_DN_VALUES returns values of the Jacobi elliptic DN function. U M DN(U,M) 0.1 0 1 0.2 0 1 0.5 0 1 1 0 1 2 0 1 0.1 0.5 0.9975093485144243 0.2 0.5 0.9901483195224799 0.5 0.5 0.9429724257773857 1 0.5 0.8231610016315963 2 0.5 0.7108610477840873 0.1 1 0.9950207489532265 0.2 1 0.9803279976447253 0.5 1 0.8868188839700739 1 1 0.6480542736638853 2 1 0.2658022288340797 4 1 0.03661899347368653 -0.2 1 0.9803279976447253 -0.5 1 0.8868188839700739 -1 1 0.6480542736638853 -2 1 0.2658022288340797 JACOBI_POLY_VALUES_TEST: JACOBI_POLY_VALUES returns values of the Jacobi polynomial. N A B X J(N,A,B)(X) 0 0 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 JACOBI_SN_VALUES_TEST: JACOBI_SN_VALUES returns values of the Jacobi elliptic SN function. U M SN(U,M) 0.1 0 0.09983341664682815 0.2 0 0.1986693307950612 0.5 0 0.479425538604203 1 0 0.8414709848078965 2 0 0.9092974268256817 0.1 0.5 0.09975068547462485 0.2 0.5 0.1980217429819704 0.5 0.5 0.4707504736556573 1 0.5 0.8030018248956439 2 0.5 0.9946623253580177 0.1 1 0.09966799462495582 0.2 1 0.197375320224904 0.5 1 0.4621171572600098 1 1 0.7615941559557649 2 1 0.9640275800758169 4 1 0.999329299739067 -0.2 1 -0.197375320224904 -0.5 1 -0.4621171572600098 -1 1 -0.7615941559557649 -2 1 -0.9640275800758169 JED_CE_VALUES_TEST: JED_CE_VALUES returns: JED, a Julian Ephemeris Date, and YMDF, the corresponding year, month, day, fraction. JED Y M D F 0 -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 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 1582 10 4 0.5 2299161 1582 10 15 0.5 2333269.5 1676 3 4 0 2361221 1752 9 13 0.5 2361222 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 2415020.31 1899 12 31 0.8100000000000001 2440587.5 1970 1 1 0 2444244.5 1980 1 6 0 2450138.5 1996 2 25 0 2451544.5 2000 1 1 0 2453073.83 2004 3 9 0.33 2456284.5 2012 12 23 0 2913943 3266 1 1 0.5 JED_MJD_VALUES_TEST: JED_MJD_VALUES returns: JED, a Julian Ephemeris Date, and MJD, the corresponding Modified Julian Day count. JED MJD 1507231.5 -892769 1660037.5 -739963 1746893.5 -653107 1770641.5 -629359 1892731.5 -507269 1931579.5 -468421 1974851.5 -425149 2091164.5 -308836 2121509.5 -278491 2155779.5 -244221 2174029.5 -225971 2191584.5 -208416 2195261.5 -204739 2229274.5 -170726 2245580.5 -154420 2266100.5 -133900 2288542.5 -111458 2290901.5 -109099 2323140.5 -76860 2334848.5 -65152 2348020.5 -51980 2366978.5 -33022 2385648.5 -14352 2392825.5 -7175 2416223.5 16223 2425848.5 25848 2430266.5 30266 2430833.5 30833 2431004.5 31004 2448698.5 48698 2450138.5 50138 2465737.5 65737 2486076.5 86076 JED_RD_VALUES_TEST: JED_RD_VALUES returns: JED, a Julian Ephemeris Date, and RD, the corresponding Reingold Dershowitz Day count. JED RD 1507231.5 -214193 1660037.5 -61387 1746893.5 25469 1770641.5 49217 1892731.5 171307 1931579.5 210155 1974851.5 253427 2091164.5 369740 2121509.5 400085 2155779.5 434355 2174029.5 452605 2191584.5 470160 2195261.5 473837 2229274.5 507850 2245580.5 524156 2266100.5 544676 2288542.5 567118 2290901.5 569477 2323140.5 601716 2334848.5 613424 2348020.5 626596 2366978.5 645554 2385648.5 664224 2392825.5 671401 2416223.5 694799 2425848.5 704424 2430266.5 708842 2430833.5 709409 2431004.5 709580 2448698.5 727274 2450138.5 728714 2465737.5 744313 2486076.5 764652 JED_WEEKDAY_VALUES_TEST: JED_WEEKDAY_VALUES returns Julian Ephemeris Dates (JED) and the corresponding weekday JED # Weekday 1507231.5 1 Sunday 1660037.5 4 Wednesday 1746893.5 4 Wednesday 1770641.5 1 Sunday 1892731.5 4 Wednesday 1931579.5 2 Monday 1974851.5 7 Saturday 2091164.5 1 Sunday 2121509.5 1 Sunday 2155779.5 6 Friday 2174029.5 7 Saturday 2191584.5 6 Friday 2195261.5 1 Sunday 2229274.5 1 Sunday 2245580.5 4 Wednesday 2266100.5 7 Saturday 2288542.5 7 Saturday 2290901.5 7 Saturday 2323140.5 4 Wednesday 2334848.5 1 Sunday 2348020.5 6 Friday 2366978.5 1 Sunday 2385648.5 2 Monday 2392825.5 4 Wednesday 2416223.5 1 Sunday 2425848.5 1 Sunday 2430266.5 2 Monday 2430833.5 2 Monday 2431004.5 5 Thursday 2448698.5 3 Tuesday 2450138.5 1 Sunday 2465737.5 4 Wednesday 2486076.5 1 Sunday KEI0_VALUES_TEST: KEI0_VALUES stores values of the Kelvin function KEI of order 0. X FX 0 0 0.5 -0.6715816950943676 1 -0.4949946365187199 1.5 -0.3313955623385585 2 -0.2024000677647043 2.5 -0.1106960991556749 3 -0.05112188404598678 3.5 -0.01600256851827124 4 0.00219839929497252 4.5 0.009720918540151989 5 0.01118758650986964 KEI1_VALUES_TEST: KEI1_VALUES stores values of the Kelvin function KEI of order 1. X FX 0.5 -1.051182085412523 1 -0.2419959664297382 1.5 0.001008680985009855 2 0.08004939780706674 2.5 0.0933137881353575 3 0.08027022252392219 3.5 0.05937625647622691 4 0.03916601076917133 4.5 0.0230021602469025 5 0.01157775439325247 KER0_VALUES_TEST: KER0_VALUES stores values of the Kelvin function KER of order 0. X FX 0.5 0.8559058721186342 1 0.286706208728316 1.5 0.05293491548771044 2 -0.04166451399150953 2.5 -0.06968797258904534 3 -0.0670292333037987 3.5 -0.05263927724224119 4 -0.03617884789954761 4.5 -0.02199987504667382 5 -0.01151172719949066 KER1_VALUES_TEST: KER1_VALUES stores values of the Kelvin function KER of order 1. X FX 0.5 -1.52240340653209 1 -0.7403222768419827 1.5 -0.4170442851662574 2 -0.230805929518123 2.5 -0.1172561358598705 3 -0.04989830778751491 3.5 -0.01272324936181659 4 0.005351296460277448 4.5 0.01209090413515866 5 0.01273739048421857 LAGUERRE_ASSOCIATED_VALUES_TEST: LAGUERRE_ASSOCIATED_VALUES stores values of the associated Laguerre polynomials. N M X L(N,M)(X) 1 0 0 1 2 0 0 1 3 0 0 1 4 0 0 1 5 0 0 1 1 1 0.5 1.5 2 1 0.5 1.625 3 1 0.5 1.479166666666667 4 1 0.5 1.1484375 3 0 0.2 0.4586666666666667 3 1 0.2 2.878666666666667 3 2 0.2 8.098666666666666 3 3 0.2 17.11866666666667 4 2 0.25 10.45328776041667 5 2 0.25 13.29019368489583 6 3 0.25 56.2245364718967 7 3 0.25 74.84729341779436 8 4 0.25 323.8912982762806 9 4 0.25 442.6100000097533 10 5 0.25 1936.87657228825 LAGUERRE_GENERAL_VALUES_TEST: LAGUERRE_GENERAL_VALUES stores values of the generalized Laguerre function. N A X L(N,A)(X) 5 0 0.25 0.03726399739583333 5 0.25 0.25 0.3494791666666667 5 0.5 0.25 0.8710042317708333 5 0.75 0.25 1.672395833333333 5 1.5 0.25 6.657625325520833 5 2.5 0.25 23.95726725260417 5 5 0.25 203.1344319661458 8 1.2 0 12.841939968 8 1.2 0.2 5.359924801587302 8 1.2 0.4 0.9204589064126985 8 1.2 0.6 -1.341585114857143 8 1.2 0.8 -2.119726307555556 8 1.2 1 -1.959193658349206 0 5.2 0.75 1 1 5.2 0.75 5.45 2 5.2 0.75 17.20125 3 5.2 0.75 41.1039375 4 5.2 0.75 82.39745859375 5 5.2 0.75 146.0179186171875 6 5.2 0.75 235.9204608298828 LAGUERRE_POLYNOMIAL_VALUES_TEST: LAGUERRE_POLYNOMIAL_VALUES stores values of the Laguerre polynomials. N X L(N)(X) 0 1 1 1 1 0 2 1 -0.5 3 1 -0.6666666666666667 4 1 -0.625 5 1 -0.4666666666666667 6 1 -0.2569444444444444 7 1 -0.04047619047619048 8 1 0.1539930555555556 9 1 0.3097442680776014 10 1 0.4189459325396825 11 1 0.4801341790925124 12 1 0.4962122235082305 5 0.5 -0.4455729166666667 5 3 0.85 5 5 -3.166666666666667 5 10 34.33333333333333 LAMBERT_W_VALUES_TEST: LAMBERT_W_VALUES stores values of the Lambert W function. X W(X) 0 0 0.5 0.3517337112491958 1 0.567143290409784 1.5 0.7258613577662263 2 0.8526055020137255 2.5 0.9585863567287028 2.718281828459045 1 3 1.04990889496404 3.5 1.130289326974136 4 1.202167873197043 4.5 1.267237814307435 5 1.3267246652422 5.5 1.381545379445041 6 1.4324047758983 6.5 1.479856830173851 7 1.524345204984144 7.5 1.566230953782388 8 1.605811996320178 10 1.745528002740699 100 3.38563014029005 1000 5.249602852401596 1000000 11.38335808614005 LAPLACE_CDF_VALUES_TEST: LAPLACE_CDF_VALUES returns values of the Laplace Cumulative Density Function. Mu Beta X CDF(X) 0 1 0 0.5 0 1 1 0.8160602794142788 0 1 2 0.9323323583816937 0 1 3 0.975106465816068 0 2 1 0.6967346701436833 0 3 1 0.6417343447131054 0 4 1 0.6105996084642976 0 5 1 0.5906346234610091 1 2 1 0.5 2 2 1 0.3032653298563167 3 2 1 0.1839397205857212 4 2 1 0.1115650800742149 LEGENDRE_ASSOCIATED_VALUES_TEST: LEGENDRE_ASSOCIATED_VALUES stores values of the associated Legendre polynomials. N M X P(N,M)(X) 1 0 0 0 2 0 0 -0.5 3 0 0 0 4 0 0 0.375 5 0 0 0 1 1 0.5 -0.8660254037844386 2 1 0.5 -1.299038105676658 3 1 0.5 -0.3247595264191645 4 1 0.5 1.353164693413185 3 0 0.2 -0.28 3 1 0.2 1.175755076535925 3 2 0.2 2.88 3 3 0.2 -14.10906091843111 4 2 0.25 -3.955078125 5 2 0.25 -9.99755859375 6 3 0.25 82.65311444100485 7 3 0.25 20.24442836815152 8 4 0.25 -423.7997531890869 9 4 0.25 1638.320624828339 10 5 0.25 -20256.87389227225 LEGENDRE_ASSOCIATED_NORMALIZED_VALUES_TEST: LEGENDRE_ASSOCIATED_NORMALIZED_VALUES stores values of the normalized associated Legendre polynomials. N M X P(N,M)(X) 0 0 0.5 0.7071067811865475 1 0 0.5 0.6123724356957945 1 1 0.5 -0.75 2 0 0.5 -0.1976423537605237 2 1 0.5 -0.8385254915624211 2 2 0.5 0.7261843774138907 3 0 0.5 -0.8184875533567997 3 1 0.5 -0.1753901900050285 3 2 0.5 0.9606516343087123 3 3 0.5 -0.6792832849776299 4 0 0.5 -0.6131941618102092 4 1 0.5 0.6418623720763665 4 2 0.5 0.4716705890038619 4 3 0.5 -1.018924927466445 4 4 0.5 0.6239615396237876 5 0 0.5 0.2107022704608181 5 1 0.5 0.8256314721961969 5 2 0.5 -0.3982651281554632 5 3 0.5 -0.7040399320721435 5 4 0.5 1.034723155272289 5 5 0.5 -0.566741212915553 LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES_TEST: LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES stores values of the associated Legendre polynomials, normalized for the unit sphere. N M X P(N,M)(X) 0 0 0.5 0.2820947917738781 1 0 0.5 0.24430125595146 1 1 0.5 -0.2992067103010745 2 0 0.5 -0.07884789131313 2 1 0.5 -0.3345232717786446 2 2 0.5 0.2897056515173922 3 0 0.5 -0.326529291016351 3 1 0.5 -0.06997056236064664 3 2 0.5 0.3832445536624809 3 3 0.5 -0.2709948227475519 4 0 0.5 -0.24462907724141 4 1 0.5 0.2560660384200185 4 2 0.5 0.1881693403754876 4 3 0.5 -0.4064922341213279 4 4 0.5 0.2489246395003027 5 0 0.5 0.0840580442633982 5 1 0.5 0.3293793022891428 5 2 0.5 -0.1588847984307093 5 3 0.5 -0.2808712959945307 5 4 0.5 0.4127948151484925 5 5 0.5 -0.2260970318780046 LEGENDRE_FUNCTION_Q_VALUES_TEST: LEGENDRE_FUNCTION_Q_VALUES stores values of the Legendre Q function. N X Q(N)(X) 0 0.25 0.2554128118829953 1 0.25 -0.9361467970292512 2 0.25 -0.4787614548274669 3 0.25 0.4246139251747229 4 0.25 0.5448396833845414 5 0.25 -0.0945132826167347 6 0.25 -0.4973516573531213 7 0.25 -0.1499018843853194 8 0.25 0.3649161918783626 9 0.25 0.3055676545072885 10 0.25 -0.1832799367995643 3 0 0.6666666666666667 3 0.1 0.626867202876333 3 0.2 0.5099015515315237 3 0.3 0.3232754180589764 3 0.4 0.08026113738148187 3 0.5 -0.1986547714794823 3 0.6 -0.4828663183349136 3 0.7 -0.7252886849144387 3 0.8 -0.8454443502398846 3 0.9 -0.6627096245052618 LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES_TEST: LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES stores values of the normalized Legendre polynomials. N X Pn(N)(X) 0 0.25 0.7071067811865475 1 0.25 0.3061862178478972 2 0.25 -0.642337649721702 3 0.25 -0.6284815141846855 4 0.25 0.3345637065282053 5 0.25 0.7967179601799685 6 0.25 0.06189376866246124 7 0.25 -0.766588850921089 8 0.25 -0.4444760242953344 9 0.25 0.5450094674858101 10 0.25 0.7167706229835538 3 0 0 3 0.1 -0.2759472322745781 3 0.2 -0.5238320341483518 3 0.3 -0.7155919752205163 3 0.4 -0.823164625090267 3 0.5 -0.8184875533567997 3 0.6 -0.6734983296193094 3 0.7 -0.360134523476992 3 0.8 0.1496662954709581 3 0.9 0.8839665576253438 3 1 1.870828693386971 LEGENDRE_POLYNOMIAL_VALUES_TEST: LEGENDRE_POLYNOMIAL_VALUES stores values of the Legendre polynomials. N X P(N)(X) 0 0.25 1 1 0.25 0.25 2 0.25 -0.40625 3 0.25 -0.3359375 4 0.25 0.15771484375 5 0.25 0.3397216796875 6 0.25 0.0242767333984375 7 0.25 -0.2799186706542969 8 0.25 -0.1524540185928345 9 0.25 0.1768244206905365 10 0.25 0.2212002165615559 3 0 0 3 0.1 -0.1475 3 0.2 -0.28 3 0.3 -0.3825 3 0.4 -0.44 3 0.5 -0.4375 3 0.6 -0.36 3 0.7 -0.1925 3 0.8 0.08 3 0.9 0.4725 3 1 1 LEGENDRE_SHIFTED_POLYNOMIAL_VALUES_TEST: LEGENDRE_SHIFTED_POLYNOMIAL_VALUES stores values of the shifted Legendre polynomials. N X P(N)(X) 0 0.625 1 1 0.625 0.25 2 0.625 -0.40625 3 0.625 -0.3359375 4 0.625 0.15771484375 5 0.625 0.3397216796875 6 0.625 0.0242767333984375 7 0.625 -0.2799186706542969 8 0.625 -0.1524540185928345 9 0.625 0.1768244206905365 10 0.625 0.2212002165615559 3 0.5 0 3 0.55 -0.1475 3 0.6 -0.28 3 0.65 -0.3825 3 0.7 -0.44 3 0.75 -0.4375 3 0.8 -0.36 3 0.85 -0.1925 3 0.9 0.08 3 0.95 0.4725 3 1 1 LERCH_VALUES_TEST: LERCH_VALUES returns values of the Lerch transcendent function. Z S A Fx 1 2 0 1.644934066848226 1 3 0 1.202056903159594 1 10 0 1.000994575127818 0.5 2 1 1.164481052930025 0.5 3 1 1.07442638721608 0.5 10 1 1.000492641212014 0.3333333333333333 2 2 0.2959190697935714 0.3333333333333333 3 2 0.1394507503935608 0.3333333333333333 10 2 0.0009823175058446061 0.1 2 3 0.1177910993911311 0.1 3 3 0.03868447922298962 0.1 10 3 1.703149614186634e-05 LOBACHEVSKY_VALUES_TEST: LOBACHEVSKY_VALUES stores values of the Lobachevsky function. X FX 0.001953125 1.241763906516139e-09 0.0078125 7.947334477000109e-08 0.03125 5.086759818620883e-06 0.125 0.000326030979012072 0.5 0.02138053681540822 1 0.1875381690208383 1.5 0.8305119997188365 2 1.885436242667903 2.5 2.131598898651641 3 2.177112018561343 4 2.292102792189665 5 3.913719502878449 6 4.351356398383643 7 4.420064496847819 10 6.565601313362383 15 10.8255046615046 20 13.36551285547423 30 21.13100268563996 50 34.83823658944912 100 69.6570624378374 LOBATTO_POLYNOMIAL_VALUES_TEST: LOBATTO_POLYNOMIAL_VALUES stores values of the completed Lobatto polynomials. N X Lo(N)(X) 1 0.25 0.9375 2 0.25 0.703125 3 0.25 -0.966796875 4 0.25 -1.50146484375 5 0.25 0.363922119140625 6 0.25 2.001914978027344 7 0.25 0.659794807434082 8 0.25 -1.934441328048706 9 0.25 -1.769941113889217 10 0.25 1.215243665501475 3 -1 0 3 -0.9 0.86925 3 -0.8 1.188 3 -0.7 1.10925 3 -0.6 0.768 3 -0.5 0.28125 3 -0.4 -0.252 3 -0.3 -0.75075 3 -0.2 -1.152 3 -0.1 -1.41075 3 0 -1.5 3 0.1 -1.41075 3 0.2 -1.152 3 0.3 -0.75075 3 0.4 -0.252 3 0.5 0.28125 3 0.6 0.768 3 0.7 1.10925 3 0.8 1.188 3 0.9 0.86925 3 1 0 LOBATTO_POLYNOMIAL_DERIVATIVES_TEST: LOBATTO_POLYNOMIAL_VALUES stores derivatives of the completed Lobatto polynomials. N X Lo'(N)(X) 1 0.25 -0.5 2 0.25 2.4375 3 0.25 4.03125 4 0.25 -3.154296875 5 0.25 -10.191650390625 6 0.25 -1.019622802734375 7 0.25 15.67544555664063 8 0.25 10.97668933868408 9 0.25 -15.91419786214828 10 0.25 -24.33202382177114 3 -1 12 3 -0.9 5.67 3 -0.8 0.96 3 -0.7 -2.31 3 -0.6 -4.32 3 -0.5 -5.25 3 -0.4 -5.28 3 -0.3 -4.59 3 -0.2 -3.36 3 -0.1 -1.77 3 0 0 3 0.1 1.77 3 0.2 3.36 3 0.3 4.59 3 0.4 5.28 3 0.5 5.25 3 0.6 4.32 3 0.7 2.31 3 0.8 -0.96 3 0.9 -5.67 3 1 -12 LOG_VALUES_TEST: LOG_VALUES stores values of the natural logarithm function. X FX 1e-05 -11.51292546497023 0.01 -4.605170185988092 0.1 -2.302585092994046 0.2 -1.6094379124341 0.3 -1.203972804325936 0.4 -0.9162907318741551 0.5 -0.6931471805599453 0.6 -0.5108256237659907 0.7 -0.3566749439387324 0.8 -0.2231435513142098 0.9 -0.1053605156578263 1 0 2 0.6931471805599453 3 1.09861228866811 3.141592653589793 1.1447298858494 5 1.6094379124341 10 2.302585092994046 20 2.995732273553991 100 4.605170185988092 123456789 18.63140176616802 LOG_NORMAL_CDF_VALUES_TEST: LOG_NORMAL_CDF_VALUES returns values of the Log Normal Cumulative Density Function. Mu Sigma X CDF(X) 1 0.5 1 0.02275013194817921 1 0.5 2 0.2697049307349095 1 0.5 3 0.5781741008028732 1 0.5 4 0.7801170895122241 1 2 2 0.4390310097476894 1 3 2 0.4592655190218048 1 4 2 0.4694258497695908 1 5 2 0.4755320473858733 2 2 3 0.3261051056816658 3 2 3 0.1708799040927608 4 2 3 0.0734325635795206 5 2 3 0.02554673736161761 LOG_SERIES_CDF_VALUES_TEST: LOG_SERIES_CDF_VALUES returns values of the Log Series Cumulative Density Function. T N CDF(X) 0.1 1 0.9491221581029903 0.1111111111111111 1 0.9433541128559735 0.125 1 0.9361094611773272 0.1428571428571429 1 0.9267370278044118 0.1666666666666667 1 0.9141358246245129 0.2 1 0.89628402354491 0.25 1 0.8690148741955517 0.3333333333333333 1 0.8221011541254772 0.5 1 0.7213475204444817 0.6666666666666667 1 0.6068261510845583 0.75 1 0.5410106403333613 0.8 1 0.4970679476476894 0.8333333333333333 1 0.465092188792706 0.8571485714857149 1 0.4404842934597863 0.875 1 0.4207860535926143 0.888888888888889 1 0.4045507673897055 0.9 1 0.3908650337129266 0.99 1 0.2149757685421097 0.99 0 0 0.99 1 0.2149757685421097 0.99 2 0.3213887739704539 0.99 3 0.3916213575531612 0.99 4 0.4437690508633213 0.99 5 0.4850700239649681 0.99 6 0.5191433267738267 0.99 7 0.5480569580144867 0.99 8 0.5731033910767085 0.99 9 0.5951442521714636 0.99 10 0.6147826594068904 LOG10_VALUES_TEST: LOG10_VALUES stores values of the base 10 logarithm function. X FX 1e-05 -5 0.01 -2 0.1 -1 0.2 -0.6989700043360189 0.3 -0.5228787452803375 0.4 -0.3979400086720376 0.5 -0.3010299956639812 0.6 -0.2218487496163564 0.7 -0.1549019599857432 0.8 -0.09691001300805642 0.9 -0.04575749056067512 1 0 2 0.3010299956639812 3 0.4771212547196624 3.141592653589793 0.4971498726941339 5 0.6989700043360189 10 1 20 1.301029995663981 100 2 123456789 8.09151497716927 LOGARITHMIC_INTEGRAL_VALUES_TEST: LOGARITHMIC_INTEGAL_VALUES stores values of the logarithmic integral function. X LI(X) 0 0 0.1 -0.03238978959329102 0.2 -0.08512648672879405 0.3 -0.1574149028946895 0.4 -0.2529494192126213 0.5 -0.378671043061088 0.6 -0.5468514142104171 0.7 -0.7809468775455607 0.8 -1.134011957382327 0.9 -1.775800683423525 0.95 -2.443622553873225 0.975 -3.124190050507211 1.03125 -2.87293551032912 1.0625 -2.164282524138207 1.125 -1.440351296279408 1.25 -0.6864884538258716 1.5 0.1250649863152964 2 1.045163780117493 4 2.967585095039051 8 5.253718299558931 16 8.51971646371106 32 13.60509217709172 64 21.934668328051 128 36.04254831722944 256 60.51306533791733 512 103.7211171690373 1024 181.0780396816945 2048 321.1144156746837 LOGISTIC_CDF_VALUES_TEST: LOGISTIC_CDF_VALUES returns values of the Logistic Cumulative Density Function. Mu Beta X CDF(X) 1 0.5 1 0.5 1 0.5 2 0.8807970779778824 1 0.5 3 0.9820137900379085 1 0.5 4 0.9975273768433652 1 2 2 0.6224593312018546 1 3 2 0.5825702064623147 1 4 2 0.5621765008857981 1 5 2 0.549833997312478 2 2 3 0.6224593312018546 3 2 3 0.5 4 2 3 0.3775406687981454 5 2 3 0.2689414213699951 MERTENS_VALUES_TEST: MERTENS_VALUES returns values of the Mertens function. N MERTENS(N) 1 1 2 0 3 -1 4 -1 5 -2 6 -1 7 -2 8 -2 9 -2 10 -1 11 -2 12 -2 100 1 1000 2 10000 -23 MITTAG_LEFFLER_EA_VALUES_TEST: MITTAG_LEFFLER_EA_VALUES stores values of the Mittag-Leffler one-parameter function E(A;X). A X E(A;X) 0.25 1 1 0.25 0.2525646348870172 0.2525646348870172 0.25 0.1427989464258737 0.1427989464258737 0.25 0.0994231091392936 0.0994231091392936 0.25 0.0762370352397216 0.0762370352397216 1.75 1 1 1.75 -0.2579027070618285 -0.2579027070618285 1.75 0.2716853059670252 0.2716853059670252 1.75 0.01846579916604009 0.01846579916604009 1.75 -0.139707389642194 -0.139707389642194 2.25 1 1 2.25 -1.022121843823497 -1.022121843823497 2.25 1.860844522589611 1.860844522589611 2.25 2.644615445996891 2.644615445996891 2.25 0.7762512036620307 0.7762512036620307 1 0.006737946999045729 0.006737946999045729 2 -0.6172728764571668 -0.6172728764571668 3 0.2010457248089053 0.2010457248089053 4 0.7922864454196143 0.7922864454196143 5 0.958340222567225 0.958340222567225 6 0.993055607747429 0.993055607747429 7 0.999007936794713 0.999007936794713 8 0.999875992064687 0.999875992064687 9 0.999986221340384 0.999986221340384 10 0.999998622134038 0.999998622134038 MOEBIUS_VALUES_TEST: MOEBIUS_VALUES returns values of the Moebius function. N MU(N) 1 1 2 -1 3 -1 4 0 5 -1 6 1 7 -1 8 0 9 0 10 1 11 -1 12 0 13 -1 14 1 15 1 16 0 17 -1 18 0 19 -1 20 0 MULTINOMIAL_PDF_VALUES_TEST: MULTINOMIAL_PDF_VALUES stores values of the Multinomial PDF. Given M possible outcomes on a single trial, with each outcome having probability P, PDF is the probability that after N trials, outcome I occurred X(I) times. N M I P X PDF() 0 0.7 2 1 0.3 1 3 2 0.441 0 0.7 2 1 0.3 2 4 2 0.2646 0 0.5 2 1 0.5 1 3 2 0.375 0 0.6 1 1 0 1 2 0.4 1 3 3 0 0 0.6 3 1 0.1 0 2 0.1 0 3 0.1 0 4 0.1 0 3 5 0.216 0 0.6 2 1 0.1 1 2 0.1 0 3 0.1 0 4 0.1 0 3 5 0.108 0 0.6 1 1 0.1 0 2 0.1 2 3 0.1 0 4 0.1 0 3 5 0.018 0 0.6 1 1 0.1 0 2 0.1 0 3 0.1 1 4 0.1 1 3 5 0.036 0 0.6 0 1 0.1 0 2 0.1 0 3 0.1 3 4 0.1 0 3 5 0.001 0 0.6 0 1 0.1 1 2 0.1 1 3 0.1 1 4 0.1 0 3 5 0.006 NEGATIVE_BINOMIAL_CDF_VALUES_TEST: NEGATIVE_BINOMIAL_CDF_VALUES stores values of the Negative Binomial Cumulative Density Function. F S P CDF(X) 4 4 0.5 0.63671875 3 5 0.5 0.36328125 2 6 0.5 0.14453125 3 4 0.5 0.5 2 5 0.5 0.2265625 1 6 0.5 0.0625 2 4 0.5 0.34375 1 5 0.5 0.109375 0 6 0.5 0.015625 2 4 0.4 0.1792 1 5 0.4 0.04096 0 6 0.4 0.004096 2 4 0.3 0.07047 1 5 0.3 0.010935 0 6 0.3 0.000729 11 1 0.3 0.986158712799 10 2 0.3 0.914974950051 9 3 0.3 0.747184652145 17 1 0.1 0.8499053647030009 16 2 0.1 0.5497160941090026 15 3 0.1 0.266204005214671 9 1 0.1 0.6513215599 8 2 0.1 0.2639010709 7 3 0.1 0.0701908264 2 0 0.01 1 1 1 0.01 0.0199 0 2 0.01 0.0001 NINE_J_VALUES_TEST: NINE_J_VALUES returns values of the Wigner 9J coefficient. J1 J2 J3 J4 J5 J6 J7 J8 J9 NINE_J 1 8 7 6.5 7.5 7.5 6 10 6 0.0004270039294528318 1.5 8 7 6.5 7.5 7.5 6 10 6 -0.001228915451058514 2 8 7 6.5 7.5 7.5 6 10 6 -0.0001944260688400887 1 3 2 4 1.5 3 3.5 2 2 0.003338419923885592 1.5 3 2 4 1.5 3 3.5 2 2 -0.0007958936865080434 2 3 2 4 1.5 3 3.5 2 2 -0.004338208690251972 0.5 0.5 1 2 1 1.5 1.5 0.5 1.5 0.05379143536399187 1 0.5 1 2 1 1.5 1.5 0.5 1.5 0.006211299937499411 1.5 0.5 1 2 1 1.5 1.5 0.5 1.5 0.03042903097250921 NORMAL_01_CDF_VALUES_TEST: NORMAL_01_CDF_VALUES stores values of the Normal 01 Cumulative Density Function. X CDF(X) 0 0.5 0.1 0.539827837277029 0.2 0.579259709439103 0.3 0.6179114221889526 0.4 0.6554217416103242 0.5 0.6914624612740131 0.6 0.725746882249927 0.7 0.758036347776927 0.8 0.7881446014166033 0.9 0.8159398746532405 1 0.8413447460685429 1.5 0.9331927987311419 2 0.9772498680518208 2.5 0.993790334674224 3 0.9986501019683699 3.5 0.9997673709209645 4 0.9999683287581669 NORMAL_01_PDF_VALUES_TEST: NORMAL_01_PDF_VALUES stores values of the Normal 01 Probability Density Function. X PDF(X) -2.252653624140994 0.03155059887555709 3.650540612071437 0.0005094586261557538 2.636073871461605 0.01235886992552887 0.4935635421351536 0.353192862601275 -0.6775433481923101 0.3171212685764107 -3.471050120671749 0.0009653372813755943 -1.939377660943641 0.06083856556197816 -3.120345651740235 0.003066504313116445 -3.649368017767143 0.0005116437388114821 1.0717256984193 0.2246444116615346 NORMAL_CDF_VALUES_TEST: NORMAL_CDF_VALUES stores values of the Normal Cumulative Density Function. X CDF(X) 1 0.5 1 0.5 1 0.5 2 0.9772498680518208 1 0.5 3 0.9999683287581669 1 0.5 4 0.9999999990134124 1 2 2 0.6914624612740131 1 3 2 0.6305586598182364 1 4 2 0.5987063256829237 1 5 2 0.579259709439103 2 2 3 0.6914624612740131 3 2 3 0.5 4 2 3 0.3085375387259869 5 2 3 0.1586552539314571 NORMAL_PDF_VALUES_TEST: NORMAL_PDF_VALUES stores values of the Normal Probability Density Function. X PDF(X) -56.31634060352484 4.785956124893755 -46.85424018542929 0.01180775937213258 12.33908855337884 2.13500469923221 6.781057314200307 0.006307849174478944 -48.48444152359102 0.6387882883091059 -50.23282168570062 0.0147514774470322 26.7931424604825 0.4024634224214489 26.67129012408019 0.9468437743011001 -19.73874370047668 3.79790008346491 -12.9643468135976 0.02140312299941794 -99.63232576831896 4.497769898408682 -103.6600156181528 0.05939959967353488 -81.09104995766396 0.1667227687589636 -80.73183222587458 0.2348929157422787 68.16949013113364 0.7032091872463158 66.09155915000321 0.007207515678571277 -47.93940044652702 4.57117016420902 -58.53544475210675 0.005944396897656727 -29.67426801922078 4.132147851761006 -35.44773135435396 0.03637663165771322 OMEGA_VALUES_TEST: OMEGA_VALUES returns values of the Omega function. N OMEGA(N) 1 0 2 1 3 1 4 1 5 1 6 2 7 1 8 1 9 1 10 2 30 3 101 1 210 4 1320 4 1764 3 2003 1 2310 5 2827 2 8717 2 12553 1 30030 6 510510 7 9699690 8 OWEN_VALUES_TEST OWEN_VALUES stores values of Owen's T function. H A T 0.0625 0.25 0.03891193023470137 6.5 0.4375 2.000577304850831e-11 7 0.96875 6.399062719389869e-13 4.78125 0.0625 1.063297480468746e-07 2 0.5 0.008625077985521507 1 0.9999975 0.0667418089782286 1 0.5 0.04306469112078537 1 1 0.06674188216570097 1 2 0.0784681869930841 1 3 0.0792995047488726 0.5 0.5 0.06448860284750375 0.5 1 0.1066710629614485 0.5 2 0.1415806036539784 0.5 3 0.1510840430760184 0.25 0.5 0.07134663382271778 0.25 1 0.1201285306350883 0.25 2 0.1666128410939293 0.25 3 0.1847501847929859 0.125 0.5 0.07317273327500386 0.125 1 0.1237630544953746 0.125 2 0.1737438887583106 0.125 3 0.1951190307092811 0.0078125 0.5 0.07378938035365545 0.0078125 1 0.1249951430754052 0.0078125 2 0.1761984774738108 0.0078125 3 0.1987772386442824 0.0078125 10 0.2340886964802671 0.0078125 100 0.2479460829231492 PARTITION_COUNT_VALUES_TEST: PARTITION_COUNT_VALUES returns values of the integer partition count function. N P(N) 0 1 1 1 2 2 3 3 4 5 5 7 6 11 7 15 8 22 9 30 10 42 11 56 12 77 13 101 14 135 15 176 16 231 17 297 18 385 19 490 20 627 PARTITION_DISTINCT_COUNT_VALUES_TEST: PARTITION_DISTINCT_COUNT_VALUES returns values of the integer distinct partition count function. N Q(N) 0 1 1 1 2 1 3 2 4 2 5 3 6 4 7 5 8 6 9 8 10 10 11 12 12 15 13 18 14 22 15 27 16 32 17 38 18 46 19 54 20 64 PHI_VALUES_TEST: PHI_VALUES returns values of the PHI function. N PHI(N) 1 1 2 1 3 2 4 2 5 4 6 2 7 6 8 4 9 6 10 4 20 8 30 8 40 16 50 20 60 16 100 40 149 148 500 200 750 200 999 648 PI_VALUES_TEST: PI_VALUES returns values of the PI function. N PI(N) 10 4 20 8 30 10 40 12 50 15 60 17 70 19 80 22 90 24 100 25 1000 168 10000 1229 100000 9592 1000000 78498 10000000 664579 100000000 5761455 1000000000 50847534 POISSON_CDF_VALUES_TEST: POISSON_CDF_VALUES returns values of the Poisson Cumulative Density Function. A X CDF(X) 0.02 0 0.9801986733067553 0.1 0 0.9048374180359596 0.1 1 0.9953211598395555 0.5 0 0.6065306597126334 0.5 1 0.9097959895689501 0.5 2 0.9856123220330293 1 0 0.3678794411714423 1 1 0.7357588823428846 1 2 0.9196986029286058 1 3 0.9810118431238462 2 0 0.1353352832366127 2 1 0.4060058497098381 2 2 0.6766764161830635 2 3 0.857123460498547 5 0 0.006737946999085467 5 1 0.0404276819945128 5 2 0.1246520194830811 5 3 0.2650259152973617 5 4 0.4404932850652124 5 5 0.6159606548330631 5 6 0.7621834629729387 POLYLOGARITHM_VALUES_TEST: POLYLOGARITHM_VALUES returns values of the polylogarithm function. N Z Fx 2 1 1.644934066848226 3 1 1.202056903159594 10 1 1.000994575127818 2 0.5 0.5822405264650125 3 0.5 0.5372131936080402 10 0.5 0.5002463206060068 2 0.3333333333333333 0.3662132299770635 3 0.3333333333333333 0.3488278611548401 10 0.3333333333333333 0.3334424797228716 2 0.1 0.1026177910993911 3 0.1 0.101288684479223 10 0.1 0.1000097826564961 POLYOMINO_CHIRAL_COUNT_VALUES_TEST: POLYOMINO_CHIRAL_COUNT_VALUES returns the number of chiral polyominoes of a given order; Order Number 0 1 1 1 2 1 3 2 4 7 5 18 6 60 7 196 8 704 9 2500 10 9189 11 33896 12 126759 13 476270 14 1802312 15 6849777 16 26152418 17 100203194 18 385221143 19 1485200848 20 5741256764 21 22245940545 22 86383382827 23 336093325058 24 1309998125640 25 5114451441106 26 19998172734786 27 78306011677182 28 307022182222506 29 1205243866707468 30 4736694001644862 POLYOMINO_FIXED_COUNT_VALUES_TEST: POLYOMINO_FIXED_COUNT_VALUES returns the number of fixed polyominoes of a given order; Order Number 0 1 1 1 2 2 3 6 4 19 5 63 6 216 7 760 8 2725 9 9910 10 36446 11 135268 12 505861 13 1903890 14 7204874 15 27394666 16 104592937 17 400795844 18 1540820542 19 5940738676 20 22964779660 21 88983512783 22 345532572678 23 1344372335524 24 5239988770268 25 20457802016011 26 79992676367108 27 313224032098244 28 1228088671826973 POLYOMINO_FREE_COUNT_VALUES_TEST: POLYOMINO_FREE_COUNT_VALUES returns the number of free polyominoes of a given order; Order Number 0 1 1 1 2 1 3 2 4 5 5 12 6 35 7 108 8 369 9 1285 10 4655 11 17073 12 63600 13 238591 14 901971 15 3426576 16 13079255 17 50107909 18 192622052 19 742624232 20 2870671950 21 11123060678 22 43191857688 23 168047007728 24 654999700403 25 2557227044764 26 9999088822075 27 39153010938487 28 153511100594603 PRANDTL_VALUES_TEST: PRANDTL_VALUES stores values of the Prandtl number of water as a function of temperature and pressure. T P Pr(T,P) 0 1 13.5 0 5 13.48 0 10 13.46 0 25 13.39 0 50 13.27 0 75 13.15 0 100 13.04 0 125 12.93 0 150 12.83 0 175 12.73 0 200 12.63 0 225 12.53 0 250 12.43 0 275 12.34 0 300 12.25 0 350 12.08 0 400 11.92 0 450 11.77 0 500 11.62 0 550 11.48 0 600 11.36 0 650 11.23 0 700 11.12 0 800 10.91 0 900 10.72 0 1000 10.55 25 1 6.137 50 1 3.555 75 1 2.378 100 1 1 150 1 0.974 200 1 0.96 400 1 0.924 600 1 0.899 800 1 0.882 PRIME_VALUES_TEST: PRIME_VALUES returns values of the prime function. N P[N] 1 2 2 3 4 7 8 19 16 53 32 131 64 311 128 719 256 1619 512 3671 1000 7919 2000 17389 4000 37813 8000 81799 16000 176081 32000 376127 64000 800573 128000 1698077 256000 3588941 512000 7559173 1024000 15881419 2048000 33283031 4096000 69600977 8192000 145253029 PSAT_VALUES_TEST: PSAT_VALUES stores values of the saturation pressure of water as a function of temperature. T PSAT(T) 0.01 0.0061173 1 0.0065716 5 0.008725999999999999 50 0.12344 100 1.0132 125 2.3201 150 4.7572 200 15.537 250 39.737 300 85.83799999999999 350 165.21 373.976 220.55 PSI_VALUES_TEST PSI_VALUES stores values of the PSI function. X PSI(X) 0.1 -10.42375494041108 0.2 -5.289039896592188 0.3 -3.502524222200133 0.4 -2.561384544585116 0.5 -1.963510026021423 0.6 -1.54061921389319 0.7 -1.220023553697935 0.8 -0.9650085667061385 0.9 -0.7549269499470515 1 -0.5772156649015329 1.1 -0.4237549404110768 1.2 -0.2890398965921883 1.3 -0.1691908888667997 1.4 -0.06138454458511615 1.5 0.03648997397857652 1.6 0.1260474527734763 1.7 0.208547874873494 1.8 0.2849914332938615 1.9 0.3561841611640597 2 0.4227843350984671 R8_FACTORIAL_VALUES_TEST: R8_FACTORIAL_VALUES stores values of the factorial function (using double arithmetic). 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 13 6227020800 14 87178291200 15 1307674368000 16 20922789888000 17 355687428096000 18 6402373705728000 19 1.21645100408832e+17 20 2.43290200817664e+18 25 1.551121004333099e+25 50 3.041409320171338e+64 100 9.332621544394415e+157 150 5.713383956445855e+262 R8_FACTORIAL_LOG_VALUES_TEST: R8_FACTORIAL_LOG_VALUES stores values of the logarithm of the factorial function (using real arithmetic). N Log(Factorial(N)) 0 0 1 0 2 0.6931471805599453 3 1.791759469228055 4 3.178053830347946 5 4.787491742782046 6 6.579251212010101 7 8.525161361065415 8 10.60460290274525 9 12.80182748008147 10 15.10441257307552 11 17.50230784587389 12 19.98721449566189 13 22.55216385312342 14 25.19122118273868 15 27.89927138384089 16 30.67186010608067 17 33.50507345013689 18 36.39544520803305 19 39.33988418719949 20 42.33561646075349 25 58.00360522298052 50 148.477766951773 100 363.7393755555635 150 605.0201058494237 500 2611.330458460156 1000 5912.128178488163 R8_FACTORIAL2_VALUES_TEST: R8_FACTORIAL2_VALUES stores values of the double factorial function (using double arithmetic). N F 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 R8_FALL_VALUES_TEST: R8_FALL_VALUES returns some exact values of the falling factorial function: X N R8_FALL(X,N) 5 4 120 5.25 4 163.16015625 5.5 4 216.5625 5.75 4 281.66015625 6 4 360 7.5 0 1 7.5 1 7.5 7.5 2 48.75 7.5 3 268.125 7.5 4 1206.5625 7.5 5 4222.96875 7.5 6 10557.421875 7.5 7 15836.1328125 7.5 8 7918.06640625 7.5 9 -3959.033203125 R8_RISE_VALUES_TEST: R8_RISE_VALUES returns some exact values of the rising factorial function: X N R8_RISE(X,N) 5 4 1680 5.25 4 1962.59765625 5.5 4 2279.0625 5.75 4 2631.97265625 6 4 3024 7.5 0 1 7.5 1 7.5 7.5 2 63.75 7.5 3 605.625 7.5 4 6359.0625 7.5 5 73129.21875 7.5 6 914115.234375 7.5 7 12340555.6640625 7.5 8 178938057.1289063 7.5 9 2773539885.498047 RAYLEIGH_CDF_VALUES_TEST: RAYLEIGH_CDF_VALUES stores values of the Rayleigh CDF. SIGMA X CDF(X) 0.5 1 0.8646647167633873 0.5 2 0.9996645373720975 0.5 3 0.9999999847700203 0.5 4 0.999999999999987 1 2 0.8646647167633873 2 2 0.3934693402873666 3 2 0.199262597083192 4 2 0.1175030974154046 5 2 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 0.08422433748856833 SECVIR_VALUES_TEST: SECVIR_VALUES stores values of the second virial coefficient of water as a function of temperature. T VIR(T) 0 -98.95999999999999 5 -90.08 10 -82.29000000000001 20 -69.36 30 -59.19 40 -51.07 60 -39.13 90 -27.81 120 -20.83 150 -16.21 180 -12.98 210 -10.63 240 -8.85 300 -6.39 400 -4.03 500 -2.71 700 -1.32 1000 -0.39 2000 0.53 SHI_VALUES_TEST: SHI_VALUES stores values of the hyperbolic sine integral function. X SHI(X) 0.5 0.5069967498196672 0.6 0.6121303965633808 0.7 0.7193380189288998 0.8 0.8289965633789345 0.9 0.9414978265114335 1 1.057250875375729 1.2 1.300250361022057 1.4 1.561713388361002 1.6 1.845814141358504 1.8 2.157290343425901 2 2.501567433354976 2.5 3.549340406224435 3 4.973440475859807 3.5 6.966162067504942 4 9.817326911233033 4.5 13.96788504934715 SI_VALUES_TEST: SI_VALUES stores values of the sine integral function. X SI(X) 0.5 0.4931074180430667 0.6 0.5881288096080801 0.7 0.6812222391166113 0.8 0.7720957854819966 0.9 0.8604707107452929 1 0.946083070367183 1.2 1.108047199013719 1.4 1.256226732779218 1.6 1.389180485870438 1.8 1.505816780255579 2 1.605412976802695 2.5 1.778520173443827 3 1.848652527999468 3.5 1.833125398665997 4 1.758203138949053 4.5 1.654140414379244 SIGMA_VALUES_TEST: SIGMA_VALUES returns values of the SIGMA function. N SIGMA(N) 1 1 2 3 3 4 4 7 5 6 6 12 7 8 8 15 9 13 10 18 30 72 127 128 128 255 129 176 210 576 360 1170 617 618 815 984 816 2232 1000 2340 SIN_VALUES_TEST: SIN_VALUES stores values of the sine function. X FX 0 0 0.2617993877991495 0.2588190451025207 0.5 0.479425538604203 0.5235987755982989 0.5 0.7853981633974483 0.7071067811865476 1 0.8414709848078965 1.047197551196598 0.8660254037844386 1.570796326794897 1 2 0.9092974268256817 3 0.1411200080598672 3.141592653589793 0 4 -0.7568024953079282 5 -0.9589242746631385 SIN_DEGREE_VALUES_TEST: SIN_DEGREE_VALUES stores values of the sine function. X FX -5 -0.08715574274765818 0 0 1 0.01745240643728351 2 0.03489949670250097 3 0.05233595624294383 4 0.0697564737441253 5 0.08715574274765818 10 0.1736481776669304 15 0.2588190451025207 30 0.5 45 0.7071067811865476 60 0.8660254037844386 75 0.9659258262890683 85 0.9961946980917455 86 0.9975640502598242 87 0.9986295347545738 88 0.9993908270190958 89 0.9998476951563913 90 1 91 0.9998476951563913 105 0.9659258262890683 180 0 SIN_POWER_INT_VALUES_TEST: SIN_POWER_INT_VALUES returns values of the integral of the N-th power of the sine function. A B N FX 10 20 0 10 0 1 1 0.4596976941318603 0 1 2 0.2726756432935796 0 1 3 0.1789405625488581 0 1 4 0.1240255653152068 0 1 5 0.08897439645157594 0 2 5 0.9039312384814995 1 2 5 0.8149568420299235 0 1 10 0.02188752242172985 0 1 11 0.01702343937406933 SINH_VALUES_TEST: SINH_VALUES stores values of the hyperbolic sine function. X FX -5 -74.20321057778875 -1 -1.175201193643801 0 0 0.1 0.100166750019844 0.2 0.201336002541094 0.3 0.3045202934471426 0.4 0.4107523258028155 0.5 0.5210953054937474 0.6 0.6366535821482413 0.7 0.7585837018395335 0.8 0.888105982187623 0.9 1.026516725708175 1 1.175201193643801 2 3.626860407847019 3 10.0178749274099 4 27.28991719712775 5 74.20321057778875 10 11013.23287470339 SIX_J_VALUES_TEST: SIX_J_VALUES returns values of the Wigner 6J coefficient. J1 J2 J3 J4 J5 J6 SIX_J 1 8 7 6.5 7.5 7.5 0.034909051383733 2 8 7 6.5 7.5 7.5 -0.03743025039659792 3 8 7 6.5 7.5 7.5 0.0189086639095956 4 8 7 6.5 7.5 7.5 0.007342448254928643 5 8 7 6.5 7.5 7.5 -0.02358935185081794 6 8 7 6.5 7.5 7.5 0.01913476955215437 7 8 7 6.5 7.5 7.5 0.001288017397724172 8 8 7 6.5 7.5 7.5 -0.01930018366290527 9 8 7 6.5 7.5 7.5 0.01677305949382889 10 8 7 6.5 7.5 7.5 0.005501147274850949 11 8 7 6.5 7.5 7.5 -0.02135439790896831 12 8 7 6.5 7.5 7.5 0.003460364451435387 13 8 7 6.5 7.5 7.5 0.02520950054795585 14 8 7 6.5 7.5 7.5 0.01483990561221713 15 8 7 6.5 7.5 7.5 0.002708577680633186 SOUND_VALUES_TEST: SOUND_VALUES stores values of the spead of sound in water as a function of temperature and pressure. T P C(T,P) 0 1 1401 100 1 472.8 200 1 533.7 300 1 585.7 350 1 609.5 400 1 632.2 500 1 674.6 600 1 713.9 850 1 802 1100 1 880.1 1600 1 1017.8 2000 1 1115.9 0 5 1401.7 0 10 1402.6 0 50 1409.6 0 100 1418.1 0 250 1443.1 0 500 1484.6 0 1000 1577.1 0 2500 1913.4 SPHERE_UNIT_AREA_VALUES_TEST: SPHERE_UNIT_AREA_VALUES stores values of the area of the unit sphere in various dimensions. N AREA 1 2 2 6.283185307179586 3 12.56637061435917 4 19.73920880217872 5 26.31894506957162 6 31.00627668029982 7 33.07336179231981 8 32.46969701133415 9 29.68658012464836 10 25.50164039877345 11 20.7251426732889 12 16.02315322625507 13 11.83817381218268 14 8.389703410491089 15 5.721649212349567 16 3.765290085742291 17 2.396678817591364 18 1.478625959000308 19 0.8858104195716824 20 0.5161378278002812 SPHERE_UNIT_VOLUME_VALUES_TEST: SPHERE_UNIT_VOLUME_VALUES stores values of the volume of the unit sphere in various dimensions. N VOLUME 1 2 2 3.141592653589793 3 4.188790204786391 4 4.934802200544679 5 5.263789013914325 6 5.16771278004997 7 4.724765970331401 8 4.058712126416768 9 3.298508902738707 10 2.550164039877345 11 1.8841038793899 12 1.335262768854589 13 0.9106287547832831 14 0.5992645293207921 15 0.3814432808233045 16 0.2353306303588932 17 0.140981106917139 18 0.08214588661112823 19 0.04662160103008855 20 0.02580689139001406 SPHERICAL_HARMONIC_VALUES_TEST: SPHERICAL_HARMONIC_VALUES stores values of the spherical harmonic function. L M THETA PHI Yr Yi 0 0 0.5236 1.047 0.2820947917738781 0 1 0 0.5236 1.047 0.4231421876608172 0 2 1 0.5236 1.047 -0.1672616358893223 -0.2897056515173922 3 2 0.5236 1.047 -0.1106331731112457 0.1916222768312404 4 3 0.5236 1.047 0.135497411373776 0 5 5 0.2618 0.6283 0.0005390423109043568 0 5 4 0.2618 0.6283 -0.005146690442951909 0.003739289485283311 5 3 0.2618 0.6283 0.0137100436134949 -0.04219517552320796 5 2 0.2618 0.6283 0.0609635202226554 0.1876264225575173 5 1 0.2618 0.6283 -0.4170400640977983 -0.3029973424491321 4 2 0.6283 0.7854 0 0.4139385503112256 4 2 1.885 0.7854 0 -0.1003229830187463 4 2 3.142 0.7854 0 0 4 2 4.398 0.7854 0 -0.1003229830187463 4 2 5.655 0.7854 0 0.4139385503112256 3 -1 0.3927 0.4488 0.3641205966137958 -0.1753512375142586 3 -1 0.3927 0.8976 0.2519792711195075 -0.3159720118970196 3 -1 0.3927 1.346 0.089930360657043 -0.3940106541811563 3 -1 0.3927 1.795 -0.089930360657043 -0.3940106541811563 3 -1 0.3927 2.244 -0.2519792711195075 -0.3159720118970196 SQRT_VALUES_TEST: SQRT_VALUES returns some exact values. X Fx 0 0 8.100000073710001e-09 9.000000040949999e-05 0.09 0.3 0.1 0.3162277660168379 0.4 0.6324555320336759 1 1 2 1.414213562373095 3 1.732050807568877 3.141592653589793 1.772453850905516 19 4.358898943540674 29 5.385164807134504 71 8.426149773176359 97 9.848857801796106 123456789 11111.11106055556 STIRLING1_VALUES_TEST: STIRLING1_VALUES returns values of the Stirling numbers of the first kind. N N S1 1 2 0 2 2 1 3 2 -3 4 2 11 5 2 -50 6 2 274 7 2 -1764 8 2 13068 9 2 -109584 10 2 1026576 8 3 -13132 8 4 6769 8 5 -1960 8 6 322 8 7 -28 8 8 1 STIRLING2_VALUES_TEST: STIRLING2_VALUES returns values of the Stirling numbers of the second kind. N N S2 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 STROMGEN_VALUES_TEST: STROMGEN_VALUES stores values of the Stromgen function. X FX 0.001953125 2.190106598569866e-16 0.0078125 2.248139943862525e-13 0.03125 2.324501957955886e-10 0.125 2.471956147597501e-07 0.5 0.0002899261098983324 1 0.01069814639080971 1.5 0.08970765096442473 2 0.4004960571959289 3 3.050410439807909 4 11.36770485843943 4.125 12.96067940532479 4.5 18.54871394474851 5 27.86627382190312 6 51.96333407169932 8 108.6101674789123 10 153.7890331655662 15 193.0266553255872 20 196.3685016600654 30 196.5194676600821 50 196.5195692086832 STRUVE_H0_VALUES_TEST: STRUVE_H0_VALUES stores values of the Struve H0 function. X H0(X) 0.001953125 0.001243397465884743 -0.0078125 -0.004973558242374842 0.0625 0.03977146905453694 -0.25 -0.1580524600165331 1 0.5686566270482879 1.25 0.6659839931489991 2 0.7908588495080959 -4 -0.1350145734224864 7.5 0.200864796681645 11 -0.1114209780026199 11.5 -0.1702680486598989 -16 -0.1354493180818647 20 0.09439369808132345 25 -0.1018248201600151 -30 0.09609842155416211 50 -0.08533767482611899 75 -0.07688229063705272 -80 0.04766383359141826 100 -0.07087875168964734 -125 0.06575290807335278 STRUVE_H1_VALUES_TEST: STRUVE_H1_VALUES stores values of the Struve H1 function. X H1(X) 0.001953125 8.095036957636753e-07 -0.0078125 1.295200972411323e-05 0.0625 0.0008287161516540709 -0.25 0.01320774837584957 1 0.1984573362019444 1.25 0.298538232318047 2 0.6467637282835621 -4 1.069726661308919 7.5 0.3883130800042056 11 0.7485424374510771 11.5 0.8466485464256736 -16 0.5838573246424439 20 0.8060058452421577 25 0.5388036213269295 -30 0.72175037834699 50 0.5800784479454419 75 0.6015191038544081 -80 0.7061151114728683 100 0.6163111032720134 -125 0.6277848076544366 STRUVE_L0_VALUES_TEST: STRUVE_L0_VALUES stores values of the Struve L0 function. X L0(X) 0.001953125 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 L1(X) 0.001953125 8.095041074986513e-07 -0.03125 0.0002072464909257151 0.125 0.003319183406689452 -0.5 0.05394218262352266 1 0.2267643810558087 2 1.102759787367716 -4 9.169277811738684 7 155.4165665242666 -10 2670.358285208483 16 865058.8017530463 16.25 1102604.661309494 -17 2284620.949415394 20 42454972.75011198 22.5 488696145.8799769 -25 5657865129.243105 30 768532038938.321 -40 1.470739616325935e+16 50 2.903078590103557e+20 60 5.844751588390468e+24 -70 1.192975078889231e+29 STUDENT_CDF_VALUES_TEST: STUDENT_CDF_VALUES returns values of the Student T Cumulative Density Function. C X CDF(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 0.8159999999999999 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 returns values of the noncentral Student T Cumulative Density Function. DF LAMBDA X CDF 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 returns values of the subfactorial function. N Subfactorial[N] 0 1 1 0 2 1 3 2 4 9 5 44 6 265 7 1854 8 14833 9 133496 10 1334961 11 14684570 12 176214841 SURTEN_VALUES_TEST: SURTEN_VALUES stores values of the surface tension of water as a function of temperature. T SIGMA(T) 10 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 Synchrotron function of order 1. X FX 0.001953125 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 Synchrotron function of order 2. X FX 0.001953125 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 tangent function. X FX 0 0 0.2617993877991495 0.2679491924311227 0.5 0.5463024898437905 0.5235987755982989 0.5773502691896257 0.7853981633974483 1 1 1.557407724654902 1.047197551196598 1.732050807568877 1.308996938995747 3.732050807568877 1.439896632895322 7.59575411272515 1.505346479845109 15.25705168826554 2 -2.185039863261519 3 -0.1425465430742778 3.141592653589793 0 4 1.157821282349577 5 -3.380515006246586 TANH_VALUES_TEST: TANH_VALUES stores values of the hyperbolic tangent function. X FX -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 returns values of the TAU function. N TAU(N) 1 1 2 2 3 2 4 3 5 2 6 4 7 2 8 4 9 3 10 4 23 2 72 12 126 12 226 4 300 18 480 24 521 2 610 8 832 14 960 28 THERCON_VALUES_TEST: THERCON_VALUES stores values of the thermal conductivity of water as a function of temperature and pressure. T P LAMBDA(T,P) 0 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 returns values of the Wigner 3J coefficient. J1 J2 J3 M1 M2 M3 THREE_J 1 4.5 3.5 1 -3.5 2.5 0.2788866755113585 2 4.5 3.5 1 -3.5 2.5 -0.09534625892455922 3 4.5 3.5 1 -3.5 2.5 -0.06741998624632421 4 4.5 3.5 1 -3.5 2.5 0.1533110351679666 5 4.5 3.5 1 -3.5 2.5 -0.156446554693686 6 4.5 3.5 1 -3.5 2.5 0.1099450412156551 7 4.5 3.5 1 -3.5 2.5 -0.05536235693131719 8 4.5 3.5 1 -3.5 2.5 0.01799835451137786 TRAN02_VALUES_TEST: TRAN02_VALUES stores values of the Transport function of order 2. X FX 0.001953125 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 Transport function of order 3. X FX 0.001953125 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 Transport function of order 4. X FX 0.001953125 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 Transport function of order 5. X FX 0.001953125 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 Transport function of order 6. X FX 0.001953125 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 Transport function of order 7. X FX 0.001953125 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 Transport function of order 8. X FX 0.001953125 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 Transport function of order 9. X FX 0.001953125 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 FX 1 1.644934066848226 1.1 1.433299150792759 1.2 1.267377205423779 1.3 1.134253434996619 1.4 1.025356590529597 1.5 0.9348022005446793 1.6 0.8584318931245799 1.7 0.7932328301639984 1.8 0.7369741375017002 1.9 0.6879720582426356 2 0.6449340668482264 TRUNCATED_NORMAL_AB_CDF_VALUES_TEST: TRUNCATED_NORMAL_AB_CDF_VALUES stores values of the Truncated Normal Cumulative Density Function. MU SIGMA A B X CDF(X) 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 TEST1547: TRUNCATED_NORMAL_AB_PDF_VALUES stores values of the Truncated Normal Probability Density Function. MU SIGMA A B X PDF(X) 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 TEST1548: TRUNCATED_NORMAL_A_CDF_VALUES stores values of the lower Truncated Normal Cumulative Density Function. MU SIGMA A X CDF(X) 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 lower Truncated Normal Probability Density Function. MU SIGMA A X PDF(X) 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 upper Truncated Normal Cumulative Density Function. MU SIGMA B X CDF(X) 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 upper Truncated Normal Probability Density Function. MU SIGMA B X PDF(X) 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 saturation temperature as a function of pressure. 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 sequence in a given base. BASE SEED VDC(BASE,SEED) 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 0.3333333333333333 3 2 0.6666666666666666 3 3 0.1111111111111111 3 4 0.4444444444444444 3 5 0.7777777777777777 3 6 0.2222222222222222 3 7 0.5555555555555556 3 8 0.8888888888888888 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 0.3703703703703703 4 10 0.625 5 10 0.08 7 10 0.4489795918367347 11 10 0.9090909090909092 13 10 0.7692307692307693 2 100 0.1484375 3 100 0.4115226337448559 4 100 0.09765625 5 100 0.032 7 100 0.2915451895043731 11 100 0.1652892561983471 13 100 0.7337278106508875 2 1000 0.0927734375 3 1000 0.3475080018289895 4 1000 0.1708984375 5 1000 0.00512 7 1000 0.9162848812994586 11 1000 0.9316303531179565 13 1000 0.9904415111515704 2 10000 0.03472900390625 3 10000 0.3861200020322105 4 10000 0.0189208984375 5 10000 0.000512 7 10000 0.5749985125245433 11 10000 0.1529950140017758 13 10000 0.2459297643639929 29 1000 0.4887449259912255 29 1001 0.5232276846119153 29 1002 0.5577104432326049 29 1003 0.5921932018532945 29 1004 0.6266759604739842 71 1000 0.0872842689942472 71 1001 0.1013687760365007 71 1002 0.1154532830787542 71 1003 0.1295377901210077 71 1004 0.1436222971632613 173 1000 0.7805138828560928 173 1001 0.786294229676902 173 1002 0.7920745764977113 173 1003 0.7978549233185205 173 1004 0.8036352701393298 409 1000 0.4449997309915651 409 1001 0.4474447187666262 409 1002 0.4498897065416874 409 1003 0.4523346943167484 409 1004 0.4547796820918096 VISCOSITY_VALUES_TEST: VISCOSITY_VALUES stores values of the viscosity of water as a function of temperature and pressure. T P ETA(T,P) 0 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(X) 0 1 -2.617993977991494 0.0253508995628118 0 1 -1.570796326794897 0.1097539041177346 0 1 0 0.5 0 1 1.047197551196598 0.8043381312498558 0 1 2.094395102393195 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 0.7853981633974483 0.625 0 1 0.7853981633974483 0.7438406999109122 0 2 0.7853981633974483 0.8369224904294019 0 3 0.7853981633974483 0.8941711407897124 0 4 0.7853981633974483 0.9291058600568743 0 5 0.7853981633974483 0.9514289900655436 WEEKDAY_VALUES_TEST: WEEKDAY_VALUES returns values of the weekday for a given Y/M/D date. Y M D W -587 7 30 1 -169 12 8 4 70 9 26 4 135 10 3 1 470 1 7 4 576 5 18 2 694 11 7 7 1013 4 19 1 1066 10 14 7 1096 5 18 1 1190 3 16 6 1240 3 3 7 1288 3 26 6 1298 4 20 1 1391 6 4 1 1436 1 25 4 1492 3 31 7 1553 9 9 7 1560 2 24 7 1648 6 10 4 1680 6 30 1 1716 7 24 6 1768 6 19 1 1819 8 2 2 1839 3 27 4 1903 4 19 1 1929 8 25 1 1941 9 29 2 1943 4 19 2 1943 10 7 5 1992 3 17 3 1996 2 25 1 2038 11 10 4 2094 7 18 1 WEIBULL_CDF_VALUES_TEST: WEIBULL_CDF_VALUES returns values of the Weibull Cumulative Density Function. Alpha Beta X CDF(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 FZ 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 returns values of the Riemann Zeta function. N ZETA(N) 2 1.644934066848226 3 1.202056903159594 4 1.082323233711138 5 1.03692775514337 6 1.017343061984449 7 1.008349277381923 8 1.004077356197944 9 1.002008392926082 10 1.000994575127818 11 1.000494188604119 12 1.000246086553308 16 1.000015282259409 20 1.000000953962034 30 1.000000000931327 40 1.000000000000909 ZETA_M1_VALUES_TEST: ZETA_M1_VALUES returns values of the Riemann Zeta Minus One function. N ZETA_M1(N) 2 0.6449340668482264 2.5 0.3414872573 3 0.2020569031595943 3.5 0.1267338673 4 0.08232323371113819 5 0.03692775514336993 6 0.01734306198444914 7 0.008349277381922827 8 0.00407735619794434 9 0.002008392926082214 10 0.0009945751278180853 11 0.0004941886041194645 12 0.0002460865533080483 16 1.528225940865187e-05 20 9.539620338728e-07 30 9.3132743242e-11 40 9.0949478e-13 TEST_VALUES_TEST: Normal end of execution. 25 June 2018 03:30:43 PM