3 December 2022 11:33:43.492 PM special_functions_test(): FORTRAN77 version. Test SPECIAL_FUNCTIONS(). MAIRYA Test AIRYA x Ai(x) Bi(x) Ai'(x) Bi'(x) 0.0 0.35502805 0.61492663 -0.25881940 0.44828836 10.0 0.11047533E-09 0.45564115E+09 -0.35206337E-09 0.14292361E+10 20.0 0.16916729E-26 0.21037650E+26 -0.75863916E-26 0.93818393E+26 30.0 0.32082176E-48 0.90572885E+47 -0.17598766E-47 0.49533045E+48 x Ai(-x) Bi(-x) Ai'(-x) Bi'(-x) 0.0 0.35502805 0.61492663 -0.25881940 0.44828836 10.0 0.40241238E-01 -0.31467983 0.99626504 0.11941411 20.0 -0.17640613 -0.20013931 0.89286286 -0.79142903 30.0 -0.87968188E-01 -0.22444694 1.2286206 -0.48369473 MAIRYB Test AIRYB x Ai(x) Bi(x) Ai'(x) Bi'(x) --------------------------------------------------------------------- 0.0 0.35502805D+00 0.61492663D+00 -0.25881940D+00 0.44828836D+00 10.0 0.11047533D-09 0.45564115D+09 -0.35206337D-09 0.14292361D+10 20.0 0.16916729D-26 0.21037650D+26 -0.75863916D-26 0.93818393D+26 30.0 0.32082176D-48 0.90572885D+47 -0.17598766D-47 0.49533045D+48 x Ai(-x) Bi(-x) Ai'(-x) Bi'(-x) --------------------------------------------------------------------- 0.0 0.35502805D+00 0.61492663D+00 -0.25881940D+00 0.44828836D+00 10.0 0.40241238D-01 -0.31467983D+00 0.99626504D+00 0.11941411D+00 20.0 -0.17640613D+00 -0.20013931D+00 0.89286286D+00 -0.79142903D+00 30.0 -0.87968188D-01 -0.22444694D+00 0.12286206D+01 -0.48369473D+00 MAIRYZO Test AIRYZO KF= 1, NT= 5 m a Ai'(a) a' Ai(a') ------------------------------------------------------------ 1 -2.33810741 0.70121082 -1.01879297 0.53565666 2 -4.08794944 -0.80311137 -3.24819758 -0.41901548 3 -5.52055983 0.86520403 -4.82009921 0.38040647 4 -6.78670809 -0.91085074 -6.16330736 -0.35790794 5 -7.94413359 0.94733571 -7.37217726 0.34230124 KF= 2, NT= 5 m b Bi'(b) b' Bi(b') ------------------------------------------------------------ 1 -1.17371322 0.60195789 -2.29443968 -0.45494438 2 -3.27109330 -0.76031014 -4.07315509 0.39652284 3 -4.83073784 0.83699101 -5.51239573 -0.36796916 4 -6.16985213 -0.88947990 -6.78129445 0.34949912 5 -7.37676208 0.92998364 -7.94017869 -0.33602624 MASWFA Test ASWFA KD = 1, m = 2, n = 3, c = 3.0 cv = 14.8277782138 x Smn(c,x) Smn'(c,x) -------------------------------------------- -1.0 -0.00000000D+00 -0.18346427D+02 -0.9 -0.17281278D+01 -0.16022896D+02 -0.8 -0.31693967D+01 -0.12646531D+02 -0.7 -0.42309376D+01 -0.84772673D+01 -0.6 -0.48490199D+01 -0.38342871D+01 -0.5 -0.49938127D+01 0.92787439D+00 -0.4 -0.46715985D+01 0.54460666D+01 -0.3 -0.39242578D+01 0.93760183D+01 -0.2 -0.28260550D+01 0.12418443D+02 -0.1 -0.14779693D+01 0.14341733D+02 0.0 0.00000000D+00 0.14999514D+02 0.1 0.14779693D+01 0.14341733D+02 0.2 0.28260550D+01 0.12418443D+02 0.3 0.39242578D+01 0.93760183D+01 0.4 0.46715985D+01 0.54460666D+01 0.5 0.49938127D+01 0.92787439D+00 0.6 0.48490199D+01 -0.38342871D+01 0.7 0.42309376D+01 -0.84772673D+01 0.8 0.31693967D+01 -0.12646531D+02 0.9 0.17281278D+01 -0.16022896D+02 1.0 0.00000000D+00 -0.18346427D+02 KD =-1, m = 2, n = 3, c = 3.0 cv = 8.8093939208 x Smn(-ic,x) Smn'(-ic,x) -------------------------------------------- -1.0 -0.00000000D+00 -0.49793299D+02 -0.9 -0.38802936D+01 -0.29012366D+02 -0.8 -0.60069892D+01 -0.14387525D+02 -0.7 -0.69050058D+01 -0.41941729D+01 -0.6 -0.69511145D+01 0.28291264D+01 -0.5 -0.64139745D+01 0.76001722D+01 -0.4 -0.54838783D+01 0.10780949D+02 -0.3 -0.42949604D+01 0.12841650D+02 -0.2 -0.29419450D+01 0.14106708D+02 -0.1 -0.14930098D+01 0.14786994D+02 0.0 0.00000000D+00 0.15001022D+02 0.1 0.14930098D+01 0.14786994D+02 0.2 0.29419450D+01 0.14106708D+02 0.3 0.42949604D+01 0.12841650D+02 0.4 0.54838783D+01 0.10780949D+02 0.5 0.64139745D+01 0.76001722D+01 0.6 0.69511145D+01 0.28291264D+01 0.7 0.69050058D+01 -0.41941729D+01 0.8 0.60069892D+01 -0.14387525D+02 0.9 0.38802936D+01 -0.29012366D+02 1.0 0.00000000D+00 -0.49793299D+02 MASWFB Test ASWFB KD = 1, m = 2, n = 3, c = 3.0 cv = 14.8277782138 x Smn(c,x) Smn'(c,x) -------------------------------------------- -1.0 0.00000000D+00 -0.18346427D+02 -0.9 -0.17281279D+01 -0.16022897D+02 -0.8 0.79609380D-02 0.31765790D-01 -0.7 0.15392602D-01 0.30841481D-01 -0.6 -0.59668631D-01 -0.47184189D-01 -0.5 -0.14615529D-01 0.27148561D-02 -0.4 -0.20409786D-01 0.23792059D-01 -0.3 -0.25576751D-01 0.61107526D-01 -0.2 -0.17584785D-01 0.77271358D-01 -0.1 -0.67940954D-02 0.65927498D-01 0.0 0.00000000D+00 0.53587672D-01 0.1 0.48205827D-02 0.46777228D-01 0.2 0.10096385D-01 0.44365703D-01 0.3 0.18039291D-01 0.43099158D-01 0.4 0.29068098D-01 0.33885212D-01 0.5 0.32547279D-01 0.60457053D-02 0.6 0.21184702D-01 -0.16752236D-01 0.7 0.12382712D-01 -0.24810697D-01 0.8 0.39000220D-01 -0.15561895D+00 0.9 -0.62871046D-02 0.58292926D-01 1.0 0.00000000D+00 0.46082817D-01 KD =-1, m = 2, n = 3, c = 3.0 cv = 8.8093939208 x Smn(-ic,x) Smn'(-ic,x) -------------------------------------------- -1.0 0.00000000D+00 0.89493435D-01 -0.9 0.69740468D-02 0.52143885D-01 -0.8 0.10796351D-01 0.25858599D-01 -0.7 0.17969336D-01 0.10914283D-01 -0.6 -0.61461708D-01 0.25018872D-01 -0.5 -0.13452501D-01 0.15941776D-01 -0.4 -0.17176097D-01 0.33769423D-01 -0.3 -0.20080156D-01 0.60041281D-01 -0.2 -0.13130041D-01 0.62960541D-01 -0.1 -0.49203627D-02 0.48732363D-01 0.0 0.00000000D+00 0.38410332D-01 0.1 0.34897970D-02 0.34563723D-01 0.2 0.75329954D-02 0.36121857D-01 0.3 0.14154807D-01 0.42324010D-01 0.4 0.24475499D-01 0.48120565D-01 0.5 0.29987938D-01 0.35536961D-01 0.6 0.21772078D-01 0.88626375D-02 0.7 0.14482557D-01 -0.87964703D-02 0.8 0.53114069D-01 -0.12721478D+00 0.9 -0.10097954D-01 0.75500860D-01 1.0 0.00000000D+00 0.89493435D-01 MBERNOA: Test BERNOA. n Bn -------------------------- 0 0.100000000000D+01 1 -0.500000000000D+00 2 0.166666666667D+00 4 -0.333333333333D-01 6 0.238095238095D-01 8 -0.333333333333D-01 10 0.757575757576D-01 MBERNOB: Test BERNOB. n Bn -------------------------- 0 0.100000000000D+01 1 -0.500000000000D+00 2 0.166666666667D+00 4 -0.333333333333D-01 6 0.238095238095D-01 8 -0.333333333333D-01 10 0.757575757576D-01 MBETA: Test BETA. p q B(p,q) --------------------------------- 1.5 2.0 0.2666666667D+00 2.5 2.0 0.1142857143D+00 1.5 3.0 0.1523809524D+00 MCCHG Test CCHG A B re(Z) im(Z) M(a,b,z) 3.3 4.25 10.0 0.0 0.61677489D+04 0.00000000D+00 3.3 4.25 25.0 0.0 0.95781844D+10 0.00000000D+00 3.3 4.25 3.0 -1.0 0.75828716D+01 -0.86815474D+01 3.3 4.25 15.0 10.0 -0.58313765D+06 -0.48195425D+05 MCERROR Test CERROR. x y Re[erf(z)] Im[erf(z)] --------------------------------------------- 1.0 2.0 -0.53664357E+00 -0.50491437E+01 2.0 2.0 0.11513109E+01 0.12729163E+00 3.0 2.0 0.99896328E+00 -0.11546724E-04 4.0 2.0 0.10000006E+01 -0.51310053E-06 5.0 2.0 0.10000000E+01 0.78344513E-10 MCERZO Test CERZO. NT= 10 n Complex zeros of erf(z) ------------------------------------- 1 1.45061616 +i 1.88094300 2 2.24465927 +i 2.61657514 3 2.83974105 +i 3.17562810 4 3.33546074 +i 3.64617438 5 3.76900557 +i 4.06069723 6 4.15899840 +i 4.43557144 7 4.51631940 +i 4.78044764 8 4.84797031 +i 5.10158804 9 5.15876791 +i 5.40333264 10 5.45219220 +i 5.68883744 MCGAMA Test CGAMA x y Re[(z)] Im[(z)] --------------------------------------------------------- 2.50 5.00 0.2267360319D-01 -0.1172284404D-01 5.00 10.00 0.1327696517D-01 0.3639011746D-02 2.50 -5.00 0.2267360319D-01 0.1172284404D-01 5.00 -10.00 0.1327696517D-01 -0.3639011746D-02 x y Re[ln(z)] Im[ln(z)] --------------------------------------------------------- 2.50 5.00 -0.3668103262D+01 0.5806009801D+01 5.00 10.00 -0.4285507444D+01 0.1911707090D+02 2.50 -5.00 -0.3668103262D+01 -0.5806009801D+01 5.00 -10.00 -0.4285507444D+01 -0.1911707090D+02 MCH12N Test CH12N n Re[Hn(1)(z)] Im[Hn(1)(z)] Re[Hn(1)'(z)] Im[Hn(1)'(z)] ---------------------------------------------------------------------------- 0 0.9066884385D-03 0.2038765027D-02 -0.2231155824D-02 0.9010280633D-03 1 0.2231155824D-02 -0.9010280633D-03 0.8723604627D-03 0.2467832204D-02 n Re[Hn(2)(z)] Im[Hn(2)(z)] Re[Hn(2)'(z)] Im[Hn(2)'(z)] ---------------------------------------------------------------------------- 0 -0.3237676597D+02 -0.3960707154D+02 -0.3491566326D+02 0.3145826281D+02 1 0.3491566326D+02 -0.3145826281D+02 -0.3013669698D+02 -0.3150390439D+02 n Re[Hn(1)(z)] Im[Hn(1)(z)] Re[Hn(1)'(z)] Im[Hn(1)'(z)] ---------------------------------------------------------------------------- 0 -0.9338278082D-05 -0.5282385958D-05 0.5670627481D-05 -0.9604545907D-05 1 -0.5670627481D-05 0.9604545907D-05 -0.9879816656D-05 -0.6120217993D-05 n Re[Hn(2)(z)] Im[Hn(2)(z)] Re[Hn(2)'(z)] Im[Hn(2)'(z)] ---------------------------------------------------------------------------- 0 0.2671853792D+03 0.5303743947D+04 0.5082773048D+04 -0.3671928694D+03 1 -0.5082773048D+04 0.3671928694D+03 0.4411208715D+03 0.4882434389D+04 n Re[Hn(1)(z)] Im[Hn(1)(z)] Re[Hn(1)'(z)] Im[Hn(1)'(z)] ---------------------------------------------------------------------------- 0 -0.3237676597D+02 0.3960707154D+02 -0.3491566326D+02 -0.3145826281D+02 1 0.3491566326D+02 0.3145826281D+02 -0.3013669698D+02 0.3150390439D+02 n Re[Hn(2)(z)] Im[Hn(2)(z)] Re[Hn(2)'(z)] Im[Hn(2)'(z)] ---------------------------------------------------------------------------- 0 0.9066884385D-03 -0.2038765027D-02 -0.2231155824D-02 -0.9010280633D-03 1 0.2231155824D-02 0.9010280633D-03 0.8723604627D-03 -0.2467832204D-02 n Re[Hn(1)(z)] Im[Hn(1)(z)] Re[Hn(1)'(z)] Im[Hn(1)'(z)] ---------------------------------------------------------------------------- 0 0.2671853792D+03 -0.5303743947D+04 0.5082773048D+04 0.3671928694D+03 1 -0.5082773048D+04 -0.3671928694D+03 0.4411208715D+03 -0.4882434389D+04 n Re[Hn(2)(z)] Im[Hn(2)(z)] Re[Hn(2)'(z)] Im[Hn(2)'(z)] ---------------------------------------------------------------------------- 0 -0.9338278082D-05 0.5282385958D-05 0.5670627481D-05 0.9604545907D-05 1 -0.5670627481D-05 -0.9604545907D-05 -0.9879816656D-05 0.6120217993D-05 MCHGM Test CHGM a b x M(a,b,x) ----------------------------------------- 1.5 2.0 20.0 0.1208527185D+09 4.5 2.0 20.0 0.1103561117D+12 -1.5 2.0 20.0 0.1004836854D+05 -4.5 2.0 20.0 -0.3936045244D+03 1.5 2.0 50.0 0.8231906643D+21 4.5 2.0 50.0 0.9310512715D+25 -1.5 2.0 50.0 0.2998662561D+16 -4.5 2.0 50.0 -0.1807604439D+13 MCHGU Test CHGU a b x U(a,b,x) -------------------------------------- -2.5 2.5 5.0 -0.90281245E+01 -1.5 2.5 5.0 0.21578056E+01 -0.5 2.5 5.0 0.17664937E+01 0.0 2.5 5.0 0.10000000E+01 0.5 2.5 5.0 0.49193496E+00 1.5 2.5 5.0 0.89442719E-01 2.5 2.5 5.0 0.12393866E-01 -2.5 5.0 10.0 -0.23198220E+01 -1.5 5.0 10.0 0.86574712E+01 -0.5 5.0 10.0 0.23799714E+01 0.0 5.0 10.0 0.10000000E+01 0.5 5.0 10.0 0.38329536E+00 1.5 5.0 10.0 0.45828172E-01 2.5 5.0 10.0 0.44453462E-02 MCIK01 Test CIK01 z = 20.00 + i 10.00 n Re[In(z)] Im[In(z)] Re[In'(z)] Im[In'(z)] ----------------------------------------------------------------- 0 -0.3877381D+08 -0.1375029D+08 -0.3785204D+08 -0.1386915D+08 1 -0.3785204D+08 -0.1386915D+08 -0.3698235D+08 -0.1395257D+08 n Re[Kn(z)] Im[Kn(z)] Re[Kn'(z)] Im[Kn'(z)] ----------------------------------------------------------------- 0 -0.3769239D-09 0.3917161D-09 0.3805638D-09 -0.4031903D-09 1 -0.3805638D-09 0.4031903D-09 0.3840826D-09 -0.4154550D-09 MCIKLV Test CIKLV v =100.00, z = 4.00 + i 2.00 Iv(z) =-0.7373606617-123 + i 0.6461109082-123 Iv'(z)=-0.8307094243-122 + i 0.2030132500-121 Kv(z) =-0.3836166007+121 + i -0.3356017795+121 Kv'(z)= 0.1103271276+123 + i 0.2886519240+122 v =100.50, z = 4.00 + i 2.00 Iv(z) =-0.1289940051-123 + i 0.6845756182-124 Iv'(z)=-0.1907996261-122 + i 0.2672465997-122 Kv(z) =-0.3008779281+122 + i -0.1593719779+122 Kv'(z)= 0.7653781978+123 + i 0.1857772148+122 MCIKNA Test CIKNA z = 4.0 + i 2.0 , Nmax = 5 n Re[In(z)] Im[In(z)] Re[In'(z)] Im[In'(z)] --------------------------------------------------------------------- 0 -0.19056142D+01 0.10403505D+02 -0.23059657D+01 0.92222463D+01 1 -0.23059657D+01 0.92222463D+01 -0.23666457D+01 0.83284588D+01 2 -0.28276772D+01 0.62534130D+01 -0.24255774D+01 0.61553456D+01 3 -0.25451891D+01 0.30884450D+01 -0.22270972D+01 0.36367893D+01 4 -0.16265172D+01 0.10201656D+01 -0.16520416D+01 0.16217056D+01 5 -0.75889410D+00 0.15496632D+00 -0.94510625D+00 0.48575220D+00 n Re[Kn(z)] Im[Kn(z)] Re[Kn'(z)] Im[Kn'(z)] --------------------------------------------------------------------- 0 -0.64221754D-02 -0.84393648D-02 0.74307276D-02 0.89585853D-02 1 -0.74307276D-02 -0.89585853D-02 0.88041795D-02 0.94880091D-02 2 -0.11186184D-01 -0.10536653D-01 0.14012532D-01 0.10936010D-01 3 -0.20594336D-01 -0.12913435D-01 0.27416815D-01 0.12106413D-01 4 -0.43647447D-01 -0.13676173D-01 0.60982763D-01 0.63953943D-02 5 -0.10137119D+00 0.12264588D-03 0.14495731D+00 -0.37132068D-01 MCIKNB Test CIKNB Nmaz = 5, z = 4.0 + i 2.0 n Re[In(z)] Im[In(z)] Re[In'(z)] Im[In'(z)] --------------------------------------------------------------------- 0 -0.19056142D+01 0.10403505D+02 -0.23059657D+01 0.92222463D+01 1 -0.23059657D+01 0.92222463D+01 -0.23666457D+01 0.83284588D+01 2 -0.28276772D+01 0.62534130D+01 -0.24255774D+01 0.61553456D+01 3 -0.25451891D+01 0.30884450D+01 -0.22270972D+01 0.36367893D+01 4 -0.16265172D+01 0.10201656D+01 -0.16520416D+01 0.16217056D+01 5 -0.75889410D+00 0.15496632D+00 -0.94510625D+00 0.48575220D+00 n Re[Kn(z)] Im[Kn(z)] Re[Kn'(z)] Im[Kn'(z)] --------------------------------------------------------------------- 0 -0.64221754D-02 -0.84393648D-02 0.74307276D-02 0.89585853D-02 1 -0.74307276D-02 -0.89585853D-02 0.88041795D-02 0.94880091D-02 2 -0.11186184D-01 -0.10536653D-01 0.14012532D-01 0.10936010D-01 3 -0.20594336D-01 -0.12913435D-01 0.27416815D-01 0.12106413D-01 4 -0.43647447D-01 -0.13676173D-01 0.60982763D-01 0.63953943D-02 5 -0.10137119D+00 0.12264588D-03 0.14495731D+00 -0.37132068D-01 MCIKVA Test CIKVA v= n+v0, v0 = 0.25, z = 4.0+ i 2.0 n Re[Iv(z)] Im[Iv(z)] Re[Iv'(z)] Im[Iv'(z)] --------------------------------------------------------------------- 0 -0.19336550D+01 0.10328998D+02 -0.23119621D+01 0.91612230D+01 1 -0.24735044D+01 0.85964317D+01 -0.23898329D+01 0.78707023D+01 n Re[Kv(z)] Im[Kv(z)] Re[Kv'(z)] Im[Kv'(z)] --------------------------------------------------------------------- 0 -0.64820386D-02 -0.84715754D-02 0.75118612D-02 0.89920077D-02 1 -0.80477525D-02 -0.92535355D-02 0.96506687D-02 0.97789903D-02 MCIKVB Test CIKVB v= n+v0, v0 = 0.25, z = 4.0+ i 2.0 n Re[Iv(z)] Im[Iv(z)] Re[Iv'(z)] Im[Iv'(z)] --------------------------------------------------------------------- 0 -0.19336550D+01 0.10328998D+02 -0.23119621D+01 0.91612230D+01 1 -0.24735044D+01 0.85964317D+01 -0.23898329D+01 0.78707023D+01 n Re[Kv(z)] Im[Kv(z)] Re[Kv'(z)] Im[Kv'(z)] --------------------------------------------------------------------- 0 -0.64820386D-02 -0.84715754D-02 0.75118612D-02 0.89920077D-02 1 -0.80477525D-02 -0.92535355D-02 0.96506687D-02 0.97789903D-02 MCISIA Test CISIA x Ci(x) Si(x) ------------------------------------ .0 - .00000000 5.0 -0.19002975 1.54993124 10.0 -0.04545643 1.65834759 20.0 0.04441982 1.54824170 30.0 -0.03303242 1.56675654 40.0 0.01902001 1.58698512 MCISIB Test CISIB, which computes the cosine and sine integrals. x ci(x) si(x) ------------------------------------ 0.0 -0.10000000+301 0.0000000 5.0 -0.19002984 1.5499311 10.0 -0.45456288E-01 1.6583479 20.0 0.44420091E-01 1.5482414 30.0 -0.33032580E-01 1.5667566 40.0 0.19020075E-01 1.5869852 MCJK Test CJK Maximum K = 15 1 0.10000000000000D+01 2 0.12500000000000D+00 3 -0.20833333333333D+00 4 0.70312500000000D-01 5 -0.40104166666667D+00 6 0.33420138888889D+00 7 0.73242187500000D-01 8 -0.89121093750000D+00 9 0.18464626736111D+01 10 -0.10258125964506D+01 11 0.11215209960938D+00 12 -0.23640869140625D+01 13 0.87891235351562D+01 14 -0.11207002616223D+02 15 0.46695844234262D+01 16 0.22710800170898D+00 17 -0.73687943594796D+01 18 0.42534998745388D+02 19 -0.91818241543240D+02 20 0.84636217674601D+02 21 -0.28212072558200D+02 22 0.57250142097473D+00 23 -0.26491430486952D+02 24 0.21819051174421D+03 25 -0.69957962737613D+03 26 0.10599904525280D+04 27 -0.76525246814118D+03 28 0.21257013003922D+03 29 0.17277275025845D+01 30 -0.10809091978839D+03 31 0.12009029132164D+04 32 -0.53056469786134D+04 33 0.11655393336865D+05 34 -0.13586550006434D+05 35 0.80617221817373D+04 36 -0.19194576623184D+04 37 0.60740420012735D+01 38 -0.49391530477309D+03 39 0.71095143024894D+04 40 -0.41192654968898D+05 41 0.12220046498302D+06 42 -0.20340017728042D+06 43 0.19254700123253D+06 44 -0.96980598388638D+05 45 0.20204291330966D+05 46 0.24380529699556D+02 47 -0.24998304818112D+04 48 0.45218768981363D+05 49 -0.33164517248456D+06 50 0.12683652733216D+07 51 -0.28135632265865D+07 52 0.37632712976564D+07 53 -0.29980159185381D+07 54 0.13117636146630D+07 55 -0.24291918790055D+06 56 0.11001714026925D+03 57 -0.13886089753717D+05 58 0.30818640461266D+06 59 -0.27856181280865D+07 60 0.13288767166422D+08 61 -0.37567176660763D+08 62 0.66344512274729D+08 63 -0.74105148211533D+08 64 0.50952602492665D+08 65 -0.19706819118432D+08 66 0.32844698530720D+07 67 0.55133589612202D+03 68 -0.84005433603024D+05 69 0.22437681779225D+07 70 -0.24474062725739D+08 71 0.14206290779753D+09 72 -0.49588978427503D+09 73 0.11068428168230D+10 74 -0.16210805521083D+10 75 0.15535968995706D+10 76 -0.93946235968158D+09 77 0.32557307418577D+09 78 -0.49329253664510D+08 79 0.30380905109224D+04 80 -0.54984232757229D+06 81 0.17395107553978D+08 82 -0.22510566188942D+09 83 0.15592798648793D+10 84 -0.65632937926193D+10 85 0.17954213731156D+11 86 -0.33026599749801D+11 87 0.41280185579754D+11 88 -0.34632043388159D+11 89 0.18688207509296D+11 90 -0.58664814920518D+10 91 0.81478909611831D+09 92 0.18257755474293D+05 93 -0.38718334425726D+07 94 0.14315787671889D+09 95 -0.21671649832238D+10 96 0.17634730606835D+11 97 -0.87867072178023D+11 98 0.28790064990615D+12 99 -0.64536486924538D+12 100 0.10081581068654D+13 101 -0.10983751560812D+13 102 0.81921866954858D+12 103 -0.39909617522447D+12 104 0.11449823773203D+12 105 -0.14679261247696D+11 106 0.11883842625678D+06 107 -0.29188388122221D+08 108 0.12470092935127D+10 109 -0.21822927757529D+11 110 0.20591450323241D+12 111 -0.11965528801962D+13 112 0.46127257808491D+13 113 -0.12320491305598D+14 114 0.23348364044582D+14 115 -0.31667088584785D+14 116 0.30565125519935D+14 117 -0.20516899410934D+14 118 0.91093411852399D+13 119 -0.24062979000285D+13 120 0.28646403571768D+12 121 0.83285930401629D+06 122 -0.23455796352225D+09 123 0.11465754899448D+11 124 -0.22961937296825D+12 125 0.24850009280341D+13 126 -0.16634824724892D+14 127 0.74373122908679D+14 128 -0.23260483118894D+15 129 0.52305488257844D+15 130 -0.85746103298290D+15 131 0.10269551960828D+16 132 -0.88949693988103D+15 133 0.54273966498766D+15 134 -0.22134963870253D+15 135 0.54177510755106D+14 136 -0.60197234172340D+13 MCJY01 Test CJY01 z = 4.00 + i 2.00 n Re[Jn(z)] Im[Jn(z)] Re[Jn'(z)] Im[Jn'(z)] -------------------------------------------------------------------- 0 -0.13787022D+01 0.39054236D+00 0.50735255D+00 0.12263041D+01 1 -0.50735255D+00 -0.12263041D+01 -0.11546013D+01 0.58506793D+00 n Re[Yn(z)] Im[Yn(z)] Re[Yn'(z)] Im[Yn'(z)] -------------------------------------------------------------------- 0 -0.38145893D+00 -0.13291649D+01 -0.12793101D+01 0.51220420D+00 1 0.12793101D+01 -0.51220420D+00 -0.58610052D+00 -0.10987930D+01 MCJYLV Test CJYLV v = 100.00, z = 4.00 + i 2.00 Jv(z) =-0.6444792518-123 + i 0.6619157435-123 Jv'(z)=-0.6251103777-122 + i 0.1967638668-121 Yv(z) = 0.2403065353+121 + i 0.2472039414+121 Yv'(z)=-0.7275814786+122 + i-0.2533588851+122 v = 100.50, z = 4.00 + i 2.00 Jv(z) =-0.1161315754-123 + i 0.7390127781-124 Jv'(z)=-0.1588519437-122 + i 0.2652227059-122 Yv(z) = 0.1941381412+122 + i 0.1237578195+122 Yv'(z)=-0.5143285247+123 + i-0.5320026773+122 MCJYNA Test CJYNA z = 4.0 + i 2.0 , Nmax = 5 n Re[Jn(z)] Im[Jn(z)] Re[Jn'(z)] Im[Jn'(z)] -------------------------------------------------------------------- 0 -0.13787022D+01 0.39054236D+00 0.50735255D+00 0.12263041D+01 1 -0.50735255D+00 -0.12263041D+01 -0.11546013D+01 0.58506793D+00 2 0.93050039D+00 -0.77959350D+00 -0.72363400D+00 -0.72836666D+00 3 0.93991546D+00 0.23042918D+00 0.29742236D+00 -0.63587637D+00 4 0.33565567D+00 0.49215925D+00 0.47452722D+00 -0.29035945D-01 5 -0.91389835D-02 0.28850107D+00 0.20054412D+00 0.19908868D+00 n Re[Yn(z)] Im[Yn(z)] Re[Yn'(z)] Im[Yn'(z)] -------------------------------------------------------------------- 0 -0.38145893D+00 -0.13291649D+01 -0.12793101D+01 0.51220420D+00 1 0.12793101D+01 -0.51220420D+00 -0.58610052D+00 -0.10987930D+01 2 0.79074211D+00 0.86842120D+00 0.78932897D+00 -0.70142425D+00 3 -0.29934789D+00 0.89064431D+00 0.70315755D+00 0.24423024D+00 4 -0.61557299D+00 0.37996071D+00 0.41126221D-01 0.34044655D+00 5 -0.38160033D+00 0.20975121D+00 -0.33884827D+00 -0.20590670D-01 z = 20.0 + i 10.0 , Nmax = 5 n Re[Jn(z)] Im[Jn(z)] Re[Jn'(z)] Im[Jn'(z)] -------------------------------------------------------------------- 0 0.15460268D+04 -0.10391216D+04 -0.10601232D+04 -0.15098284D+04 1 0.10601232D+04 0.15098284D+04 0.14734253D+04 -0.10783122D+04 2 -0.14008238D+04 0.11175029D+04 0.11274890D+04 0.13643952D+04 3 -0.11948548D+04 -0.12189620D+04 -0.11843035D+04 0.11920871D+04 4 0.96778325D+03 -0.12666712D+04 -0.12483664D+04 -0.93887194D+03 5 0.13018781D+04 0.65878188D+03 0.64152944D+03 -0.12682398D+04 n Re[Yn(z)] Im[Yn(z)] Re[Yn'(z)] Im[Yn'(z)] -------------------------------------------------------------------- 0 0.10391216D+04 0.15460268D+04 0.15098284D+04 -0.10601232D+04 1 -0.15098284D+04 0.10601232D+04 0.10783122D+04 0.14734253D+04 2 -0.11175029D+04 -0.14008238D+04 -0.13643952D+04 0.11274890D+04 3 0.12189620D+04 -0.11948548D+04 -0.11920871D+04 -0.11843035D+04 4 0.12666712D+04 0.96778324D+03 0.93887194D+03 -0.12483664D+04 5 -0.65878189D+03 0.13018781D+04 0.12682398D+04 0.64152944D+03 MCJYNB Test CJYNB z = 4.0 + i 2.0 , Nmax = 5 n Re[Jn(z)] Im[Jn(z)] Re[Jn'(z)] Im[Jn'(z)] -------------------------------------------------------------------- 0 -0.13787022D+01 0.39054236D+00 0.50735255D+00 0.12263041D+01 1 -0.50735255D+00 -0.12263041D+01 -0.11546013D+01 0.58506793D+00 2 0.93050039D+00 -0.77959350D+00 -0.72363400D+00 -0.72836666D+00 3 0.93991546D+00 0.23042918D+00 0.29742236D+00 -0.63587637D+00 4 0.33565567D+00 0.49215925D+00 0.47452722D+00 -0.29035945D-01 5 -0.91389835D-02 0.28850107D+00 0.20054412D+00 0.19908868D+00 n Re[Yn(z)] Im[Yn(z)] Re[Yn'(z)] Im[Yn'(z)] -------------------------------------------------------------------- 0 -0.38145893D+00 -0.13291649D+01 -0.12793101D+01 0.51220420D+00 1 0.12793101D+01 -0.51220420D+00 -0.58610052D+00 -0.10987930D+01 2 0.79074211D+00 0.86842120D+00 0.78932897D+00 -0.70142425D+00 3 -0.29934789D+00 0.89064431D+00 0.70315755D+00 0.24423024D+00 4 -0.61557299D+00 0.37996071D+00 0.41126221D-01 0.34044655D+00 5 -0.38160033D+00 0.20975121D+00 -0.33884827D+00 -0.20590670D-01 z = 20.0 + i 10.0 , Nmax = 5 n Re[Jn(z)] Im[Jn(z)] Re[Jn'(z)] Im[Jn'(z)] -------------------------------------------------------------------- 0 0.15460268D+04 -0.10391216D+04 -0.10601232D+04 -0.15098284D+04 1 0.10601232D+04 0.15098284D+04 0.14734253D+04 -0.10783122D+04 2 -0.14008238D+04 0.11175029D+04 0.11274890D+04 0.13643952D+04 3 -0.11948548D+04 -0.12189620D+04 -0.11843035D+04 0.11920871D+04 4 0.96778325D+03 -0.12666712D+04 -0.12483664D+04 -0.93887194D+03 5 0.13018781D+04 0.65878188D+03 0.64152944D+03 -0.12682398D+04 n Re[Yn(z)] Im[Yn(z)] Re[Yn'(z)] Im[Yn'(z)] -------------------------------------------------------------------- 0 0.10391216D+04 0.15460268D+04 0.15098284D+04 -0.10601232D+04 1 -0.15098284D+04 0.10601232D+04 0.10783122D+04 0.14734253D+04 2 -0.11175029D+04 -0.14008238D+04 -0.13643952D+04 0.11274890D+04 3 0.12189620D+04 -0.11948548D+04 -0.11920871D+04 -0.11843035D+04 4 0.12666712D+04 0.96778324D+03 0.93887194D+03 -0.12483664D+04 5 -0.65878189D+03 0.13018781D+04 0.12682398D+04 0.64152944D+03 MCJYVA Test CJYVA v = n+v0, v0 = 0.33, z = 4.00 + 2.00i n Re[Jv(z)] Im[Jv(z)] Re[Jv'(z)] Im[Jv'(z)] --------------------------------------------------------------------- 0 -0.13829878D+01 -0.30855145D+00 -0.18503756D+00 0.13103689D+01 n Re[Yv(z)] Im[Yv(z)] Re[Yv'(z)] Im[Yv'(z)] --------------------------------------------------------------------- 0 0.34099851D+00 -0.13440666D+01 -0.13544477D+01 -0.15470699D+00 MCJYVB Test CJYVB v = n+v0, v0 = 0.33, z = 4.00 + 2.00i n Re[Jv(z)] Im[Jv(z)] Re[Jv'(z)] Im[Jv'(z)] --------------------------------------------------------------------- 0 -0.13829878D+01 -0.30855145D+00 -0.18503756D+00 0.13103689D+01 1 0.82553327D-01 -0.12848394D+01 -0.12336901D+01 0.45079506D-01 n Re[Yv(z)] Im[Yv(z)] Re[Yv'(z)] Im[Yv'(z)] --------------------------------------------------------------------- 0 0.34099851D+00 -0.13440666D+01 -0.13544477D+01 -0.15470699D+00 1 0.13323787D+01 0.53735934D-01 -0.21467271D-01 -0.11807457D+01 MCLPMN Test CLPMN m = 0, n = 5, x = 0.5, y = 0.2 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 0 0 0.100000D+01 0.000000D+00 0.000000D+00 0.000000D+00 0 1 0.500000D+00 0.200000D+00 0.100000D+01 0.000000D+00 0 2 -0.185000D+00 0.300000D+00 0.150000D+01 0.600000D+00 0 3 -0.587500D+00 0.550000D-01 0.750000D-01 0.150000D+01 0 4 -0.394562D+00 -0.382500D+00 -0.261250D+01 0.985000D+00 0 5 0.252594D+00 -0.530293D+00 -0.347606D+01 -0.194250D+01 m = 1, n = 5, x = 0.5, y = 0.2 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 1 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 1 1 -0.895802D+00 0.111632D+00 0.522227D+00 0.288342D+00 1 2 -0.141068D+01 -0.370034D+00 -0.207707D+01 0.108074D+01 1 3 -0.234633D+00 -0.133533D+01 -0.744676D+01 -0.104520D+01 1 4 0.223033D+01 -0.117400D+01 -0.597817D+01 -0.925132D+01 1 5 0.333071D+01 0.135206D+01 0.117643D+02 -0.144329D+02 m = 2, n = 5, x = 0.5, y = 0.2 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 2 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 2 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 2 2 0.237000D+01 -0.600000D+00 -0.300000D+01 -0.120000D+01 2 3 0.652500D+01 0.870000D+00 0.555000D+01 -0.900000D+01 2 4 0.488475D+01 0.759000D+01 0.463500D+02 -0.582000D+01 2 5 -0.102769D+02 0.125758D+02 0.765712D+02 0.598500D+02 m = 3, n = 5, x = 0.5, y = 0.2 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 3 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 3 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 3 2 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 3 3 -0.102804D+02 0.401024D+01 0.211602D+02 0.555051D+01 3 4 -0.415956D+02 -0.356654D+00 -0.567241D+01 0.771228D+02 3 5 -0.572879D+02 -0.522744D+02 -0.343414D+03 0.147389D+03 m = 4, n = 5, x = 0.5, y = 0.2 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 4 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 2 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 3 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 4 0.613305D+02 -0.331800D+02 -0.182700D+03 -0.243600D+02 4 5 0.335711D+03 -0.389151D+02 -0.226327D+03 -0.737100D+03 m = 5, n = 5, x = 0.5, y = 0.2 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 5 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 2 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 3 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 4 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 5 -0.461125D+03 0.329122D+03 0.187180D+04 0.160494D+02 m = 0, n = 5, x = 2.5, y = 1.0 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 0 0 0.100000D+01 0.000000D+00 0.000000D+00 0.000000D+00 0 1 0.250000D+01 0.100000D+01 0.100000D+01 0.000000D+00 0 2 0.737500D+01 0.750000D+01 0.750000D+01 0.300000D+01 0 3 0.165625D+02 0.428750D+02 0.378750D+02 0.375000D+02 0 4 -0.810156D+01 0.210938D+03 0.123437D+03 0.303125D+03 0 5 -0.429395D+03 0.900336D+03 -0.350391D+02 0.193594D+04 m = 1, n = 5, x = 2.5, y = 1.0 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 1 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 1 1 0.232510D+01 0.107522D+01 0.104964D+01 -0.553094D-01 1 2 0.142126D+02 0.150395D+02 0.150136D+02 0.595978D+01 1 3 0.477424D+02 0.127915D+03 0.112892D+03 0.112464D+03 1 4 -0.389217D+02 0.837519D+03 0.487504D+03 0.120998D+04 1 5 -0.216303D+04 0.446358D+04 -0.208935D+03 0.964685D+04 m = 2, n = 5, x = 2.5, y = 1.0 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 2 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 2 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 2 2 0.127500D+02 0.150000D+02 0.150000D+02 0.600000D+01 2 3 0.843750D+02 0.251250D+03 0.221250D+03 0.225000D+03 2 4 -0.172969D+03 0.245625D+04 0.140625D+04 0.360750D+04 2 5 -0.883477D+04 0.174005D+05 -0.123703D+04 0.381938D+05 m = 3, n = 5, x = 2.5, y = 1.0 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 3 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 3 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 3 2 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 3 3 0.675837D+02 0.242928D+03 0.213189D+03 0.225592D+03 3 4 -0.517782D+03 0.472433D+04 0.262475D+04 0.714068D+04 3 5 -0.273211D+05 0.499684D+05 -0.568080D+04 0.112614D+06 m = 4, n = 5, x = 2.5, y = 1.0 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 4 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 2 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 3 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 4 4 -0.728437D+03 0.446250D+04 0.236250D+04 0.703500D+04 4 5 -0.565523D+05 0.938503D+05 -0.167147D+05 0.219713D+06 m = 5, n = 5, x = 2.5, y = 1.0 m n Re[Pmn(z)] Im[Pmn(z)] Re[Pmn'(z)] Im[Pmn'(z)] ------------------------------------------------------------------ 5 0 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 1 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 2 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 3 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 4 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00 5 5 -0.584268D+05 0.863328D+05 -0.233002D+05 0.212595D+06 MCLPN Test CLPN x = 3.0, y = 2.0 n Re[Pn(z)] Im[Pn(z)] Re[Pn'(z)] Im[Pn'(z)] ----------------------------------------------------------- 0 0.100000D+01 0.000000D+00 0.000000D+00 0.000000D+00 1 0.300000D+01 0.200000D+01 0.100000D+01 0.000000D+00 2 0.700000D+01 0.180000D+02 0.900000D+01 0.600000D+01 3 -0.270000D+02 0.112000D+03 0.360000D+02 0.900000D+02 4 -0.539000D+03 0.480000D+03 -0.180000D+03 0.790000D+03 5 -0.461700D+04 0.562000D+03 -0.481500D+04 0.441000D+04 MCLQMN Test CLQMN m = 0, n = 5, x = 0.5, y = 0.2 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 0 0 0.516607D+00 0.256529D+00 0.118958D+01 0.301159D+00 0 1 -0.793003D+00 0.231586D+00 0.105116D+01 0.645025D+00 0 2 -0.922531D+00 -0.192476D+00 -0.118943D+01 0.995917D+00 0 3 -0.175949D+00 -0.622297D+00 -0.356149D+01 -0.317355D+00 0 4 0.755747D+00 -0.461735D+00 -0.242107D+01 -0.336016D+01 0 5 0.987156D+00 0.354345D+00 0.324023D+01 -0.447297D+01 m = 1, n = 5, x = 0.5, y = 0.2 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 1 0 -0.109925D+01 -0.136984D+00 -0.534394D+00 -0.500279D+00 1 1 -0.101364D+01 -0.460471D+00 -0.216982D+01 -0.348062D+00 1 2 0.954316D+00 -0.102492D+01 -0.501803D+01 -0.220484D+01 1 3 0.322582D+01 -0.113288D+00 0.470405D+00 -0.730527D+01 1 4 0.254390D+01 0.273978D+01 0.181755D+02 -0.562785D+01 1 5 -0.240328D+01 0.436861D+01 0.281158D+02 0.171437D+02 m = 2, n = 5, x = 0.5, y = 0.2 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 2 0 0.106912D+01 0.776991D+00 0.291845D+01 0.226371D+01 2 1 0.237916D+01 0.602319D+00 0.207560D+01 0.249254D+01 2 2 0.394739D+01 0.167500D+01 0.767647D+01 0.874192D+00 2 3 -0.132316D+01 0.572562D+01 0.297515D+02 0.826681D+01 2 4 -0.161919D+02 0.490611D+01 0.224562D+02 0.531472D+02 2 5 -0.245853D+02 -0.138072D+02 -0.106283D+03 0.913792D+02 m = 3, n = 5, x = 0.5, y = 0.2 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 3 0 -0.353562D+01 -0.313011D+01 -0.843460D+01 -0.151438D+02 3 1 -0.427515D+01 -0.400223D+01 -0.123225D+02 -0.153529D+02 3 2 -0.101311D+02 -0.395202D+01 -0.116410D+02 -0.181454D+02 3 3 -0.228905D+02 -0.930131D+01 -0.393011D+02 -0.491912D+01 3 4 -0.630819D+01 -0.408891D+02 -0.221055D+03 -0.284751D+02 3 5 0.102723D+03 -0.651233D+02 -0.362578D+03 -0.429802D+03 m = 4, n = 5, x = 0.5, y = 0.2 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 4 0 0.120778D+02 0.205865D+02 0.353270D+02 0.109889D+03 4 1 0.159882D+02 0.223459D+02 0.409732D+02 0.122477D+03 4 2 0.249072D+02 0.299104D+02 0.703485D+02 0.137053D+03 4 3 0.635714D+02 0.343923D+02 0.824853D+02 0.172328D+03 4 4 0.175713D+03 0.703482D+02 0.255730D+03 0.569846D+02 4 5 0.155510D+03 0.357712D+03 0.196975D+04 -0.287414D+02 m = 5, n = 5, x = 0.5, y = 0.2 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 5 0 -0.453987D+02 -0.151428D+03 -0.363245D+02 -0.978606D+03 5 1 -0.580010D+02 -0.170260D+03 -0.855484D+02 -0.104930D+04 5 2 -0.958490D+02 -0.206127D+03 -0.181735D+03 -0.124519D+04 5 3 -0.186255D+03 -0.290327D+03 -0.455223D+03 -0.150989D+04 5 4 -0.521355D+03 -0.372112D+03 -0.670655D+03 -0.200730D+04 5 5 -0.167357D+04 -0.680954D+03 -0.193093D+04 -0.925757D+03 m = 0, n = 5, x = 2.5, y = 1.0 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 0 0 0.351336D+00 -0.154851D+00 -0.986938D-01 0.116110D+00 0 1 0.331906D-01 -0.357930D-01 -0.115091D-01 0.367305D-01 0 2 0.248638D-02 -0.701232D-02 0.877950D-03 0.873118D-02 0 3 -0.799384D-04 -0.121199D-02 0.922836D-03 0.166895D-02 0 4 -0.935391D-04 -0.183096D-03 0.318382D-03 0.247275D-03 0 5 -0.274023D-04 -0.227141D-04 0.809834D-04 0.210884D-04 m = 1, n = 5, x = 2.5, y = 1.0 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 1 0 -0.354317D+00 0.163851D+00 0.971713D-01 -0.127333D+00 1 1 -0.662532D-01 0.730275D-01 0.218394D-01 -0.754313D-01 1 2 -0.734663D-02 0.212449D-01 -0.301248D-02 -0.264680D-01 1 3 0.351192D-03 0.487274D-02 -0.378386D-02 -0.669673D-02 1 4 0.474395D-03 0.917271D-03 -0.161072D-02 -0.123290D-02 1 5 0.165620D-03 0.136108D-03 -0.489095D-03 -0.124400D-03 m = 2, n = 5, x = 2.5, y = 1.0 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 2 0 0.725689D+00 -0.383164D+00 -0.182423D+00 0.323896D+00 2 1 0.197388D+00 -0.232221D+00 -0.542635D-01 0.244152D+00 2 2 0.279909D-01 -0.874857D-01 0.167205D-01 0.109137D+00 2 3 -0.223553D-02 -0.247343D-01 0.203279D-01 0.337824D-01 2 4 -0.296814D-02 -0.553506D-02 0.100057D-01 0.733040D-02 2 5 -0.118481D-02 -0.948832D-03 0.349090D-02 0.825057D-03 m = 3, n = 5, x = 2.5, y = 1.0 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 3 0 -0.225346D+01 0.144159D+01 0.458360D+00 -0.133639D+01 3 1 -0.777371D+00 0.101867D+01 0.133167D+00 -0.109716D+01 3 2 -0.127553D+00 0.458488D+00 -0.124668D+00 -0.572390D+00 3 3 0.183701D-01 0.152082D+00 -0.136474D+00 -0.205373D+00 3 4 0.222256D-01 0.390936D-01 -0.740825D-01 -0.504283D-01 3 5 0.982179D-02 0.753264D-02 -0.288271D-01 -0.596384D-02 m = 4, n = 5, x = 2.5, y = 1.0 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 4 0 0.935943D+01 -0.752779D+01 -0.106853D+01 0.753793D+01 4 1 0.376818D+01 -0.574451D+01 0.183988D-01 0.634208D+01 4 2 0.651161D+00 -0.292982D+01 0.112055D+01 0.365119D+01 4 3 -0.179575D+00 -0.110010D+01 0.110367D+01 0.145905D+01 4 4 -0.194501D+00 -0.316321D+00 0.638945D+00 0.391729D+00 4 5 -0.927915D-01 -0.669521D-01 0.270840D+00 0.451376D-01 m = 5, n = 5, x = 2.5, y = 1.0 m n Re[Qmn(z)] Im[Qmn(z)] Re[Qmn'(z)] Im[Qmn'(z)] ----------------------------------------------------------------- 5 0 -0.482203D+02 0.500542D+02 -0.212065D+01 -0.529847D+02 5 1 -0.213264D+02 0.397182D+02 -0.644553D+01 -0.447361D+02 5 2 -0.340621D+01 0.221394D+02 -0.115372D+02 -0.274017D+02 5 3 0.199468D+01 0.915824D+01 -0.104405D+02 -0.118215D+02 5 4 0.195103D+01 0.288289D+01 -0.630115D+01 -0.336129D+01 5 5 0.985601D+00 0.656737D+00 -0.285567D+01 -0.332533D+00 MCLQN Test CLQN x = 0.5, y = 0.5 n Re[Qn(z)] Im[Qn(z)] Re[Qn'(z)] Im[Qn'(z)] ----------------------------------------------------------- 0 0.402359D+00 0.553574D+00 0.800000D+00 0.400000D+00 1 -0.107561D+01 0.477967D+00 0.602359D+00 0.115357D+01 2 -0.136636D+01 -0.725018D+00 -0.242682D+01 0.183390D+01 3 0.182619D+00 -0.206146D+01 -0.622944D+01 -0.247151D+01 4 0.298834D+01 -0.110022D+01 -0.114849D+01 -0.125963D+02 5 0.353361D+01 0.334847D+01 0.206656D+02 -0.123735D+02 x = 3.0, y = 2.0 n Re[Qn(z)] Im[Qn(z)] Re[Qn'(z)] Im[Qn'(z)] ----------------------------------------------------------- 0 0.229073D+00 -0.160875D+00 -0.250000D-01 0.750000D-01 1 0.896860D-02 -0.244805D-01 0.407268D-02 0.141247D-01 2 -0.736230D-03 -0.281865D-02 0.190581D-02 0.155860D-02 3 -0.264727D-03 -0.227023D-03 0.391535D-03 0.314880D-04 4 -0.430648D-04 -0.443187D-05 0.527190D-04 -0.305592D-04 5 -0.481362D-05 0.265297D-05 0.395108D-05 -0.839883D-05 MCOMELP Test COMELP k K(k) E(K) --------------------------------- 0.00 1.570796 1.570796 0.25 1.596242 1.545957 0.50 1.685750 1.467462 0.75 1.910990 1.318472 1.00 1.000000 MCPBDN Test CPBDN N = 5, z =x+iy : 5.00+ 5.00 i n Re[Dn(z)] Im[Dn(z)] Re[Dn'(z)] Im[Dn'(z)] -------------------------------------------------------------------- 0 0.99779828D+00 0.66321897D-01 -0.23286910D+01 -0.26603004D+01 1 0.46573819D+01 0.53206009D+01 0.26558457D+01 -0.24878635D+02 2 -0.43138931D+01 0.49823592D+02 0.14465848D+03 -0.10313305D+03 3 -0.28000219D+03 0.21690729D+03 0.12293320D+04 0.30720802D+03 4 -0.24716057D+04 -0.46494526D+03 0.38966424D+04 0.82090067D+04 5 -0.89132936D+04 -0.15550384D+05 -0.28950755D+05 0.58834468D+05 N = -5, z =x+iy : 5.00+ 5.00 i -n Re[Dn(z)] Im[Dn(z)] Re[Dn'(z)] Im[Dn'(z)] -------------------------------------------------------------------- 0 0.99779828D+00 0.66321897D-01 -0.23286910D+01 -0.26603004D+01 1 0.10813809D+00 -0.90921592D-01 -0.50014908D+00 -0.23280660D-01 2 0.24998820D-02 -0.19760577D-01 -0.52486940D-01 0.47769856D-01 3 -0.15821033D-02 -0.23090595D-02 -0.68249161D-03 0.10032670D-01 4 -0.37829961D-03 -0.10158757D-03 0.89032322D-03 0.11093416D-02 5 -0.49635781D-04 0.22594094D-04 0.19772492D-03 0.33983350D-04 MCPSI Test CPSI x y Re[Psi(z)] Im[Psi(z)] ---------------------------------------------- 3.0 2.0 0.11645915E+01 0.67080728E+00 3.0 -2.0 0.11645915E+01 -0.67080728E+00 -3.0 2.0 0.13953607E+01 0.26246534E+01 -3.0 -2.0 0.13953607E+01 -0.26246534E+01 MCSPHIK Test CSPHIK Nmaz = 5, z = 4.0+ i 2.0 n Re[in(z)] Im[in(z)] Re[in'(z)] Im[in'(z)] ------------------------------------------------------------------------ 0 0.21180804D+00 0.61019224D+01 -0.44393565D+00 0.49001501D+01 1 -0.44393565D+00 0.49001501D+01 -0.59064772D+00 0.40530753D+01 2 -0.99187560D+00 0.30286517D+01 -0.75740580D+00 0.27853964D+01 3 -0.96638590D+00 0.13755606D+01 -0.76899111D+00 0.15416489D+01 4 -0.60182775D+00 0.42639674D+00 -0.57775652D+00 0.64824997D+00 5 -0.26685302D+00 0.66401477D-01 -0.32144501D+00 0.18660316D+00 n Re[kn(z)] Im[kn(z)] Re[kn'(z)] Im[kn'(z)] ------------------------------------------------------------------------ 0 -0.50105817D-02 -0.40348623D-02 0.64161842D-02 0.43407766D-02 1 -0.64161842D-02 -0.43407766D-02 0.84452107D-02 0.44879361D-02 2 -0.10162525D-01 -0.47144730D-02 0.13928041D-01 0.41207029D-02 3 -0.18935946D-01 -0.39739871D-02 0.26900877D-01 0.31928431D-03 4 -0.39454641D-01 0.29771072D-02 0.56902033D-01 -0.18730440D-01 5 -0.87274902D-01 0.36893982D-01 0.12204813D+00 -0.99614828D-01 MSPHJY CSPHJY computes spherical Bessel functions jn(z), yn(z) and their derivatives. n Re[jn(z)] Im[jn(z)] Re[jn'(z)] Im[jn'(z)] -------------------------------------------- ---------------------------- 0 -0.80651523D+00 -0.18941093D+00 -0.37101203D-01 0.75210758D+00 1 0.37101203D-01 -0.75210758D+00 -0.67093420D+00 0.11885235D+00 2 0.60314368D+00 -0.27298399D+00 -0.24288981D+00 -0.40737409D+00 3 0.42955048D+00 0.17755176D+00 0.18848259D+00 -0.24320520D+00 4 0.12251323D+00 0.22087111D+00 0.19660170D+00 0.17937264D-01 5 -0.10242676D-01 0.10975433D+00 0.68951842D-01 0.83020305D-01 n Re[yn(z)] Im[yn(z)] Re[yn'(z)] Im[yn'(z)] -------------------------------------------- ---------------------------- 0 0.21734534D+00 -0.79487692D+00 -0.77049661D+00 -0.87010064D-02 1 0.77049661D+00 0.87010064D-02 -0.92593503D-01 -0.64425800D+00 2 0.24756293D+00 0.56894854D+00 0.45127429D+00 -0.25839924D+00 3 -0.23845941D+00 0.43646607D+00 0.26374403D+00 0.12439192D+00 4 -0.27587985D+00 0.20902555D+00 -0.67092335D-01 0.89500599D-01 5 -0.70001327D-01 0.18807178D+00 -0.30472133D+00 -0.58661384D-01 MCVA1 Test CVA1 Mmax = 12, q = 25.00 Characteristic values of Mathieu functions m a b ------------------------------------------ 0 -40.256779547 1 -21.314899691 -40.256778985 2 -3.522164727 -21.314860622 3 12.964079444 -3.520941527 4 27.805240581 12.986489953 5 40.050190986 28.062765899 6 48.975786716 41.801071292 7 57.534689001 55.002957151 8 69.524065166 69.057988351 9 85.076999882 85.023356505 10 103.230204804 103.225680042 11 123.643012376 123.642713667 12 146.207690643 146.207674647 MCVA2 Test CVA2 m a b ----------------------------------- 0 -40.25677955 1 -21.31489969 -40.25677897 2 -3.52216473 -21.31485362 3 12.96407944 -3.52096113 4 27.80524058 12.98203059 5 40.05019099 27.98662419 6 48.97578672 41.18383174 7 57.53468900 52.11053599 8 69.52406517 52.11053599 9 85.07699988 85.04721138 10 103.23020480 103.22740759 11 123.64301238 123.64274216 12 146.20769064 146.20765035 MCYZO Test CYZO NT= 5, KF= 0, KC= 0 No. z0, Zeros of Y0(z) Y1(z0) ------------------------------------------------------------------ 1 -2.403016632 0.5398823130 0.1007476893 -0.8819677101 2 -5.519876702 0.5471800106 -0.0292464182 0.5871695027 3 -8.653672403 0.5484120673 0.0149080637 -0.4694587524 4 -11.791512030 0.5488191184 -0.0093736817 0.4023045429 5 -14.930906564 0.5490008289 0.0065788031 -0.3575673214 NT= 5, KF= 1, KC= 0 No. z1, Zeros of Y1(z) Y0(z1) ------------------------------------------------------------------ 1 -0.502743273 0.7862437145 -0.4595276847 1.3171019361 2 -3.833535193 0.5623565382 0.0483019087 -0.6925128842 3 -7.015903683 0.5533930459 -0.0201269494 0.5186425332 4 -10.173573834 0.5512733877 0.0116140017 -0.4320329636 5 -13.323739307 0.5504585830 -0.0077719300 0.3779698048 NT= 5, KF= 2, KC= 0 No. z1', Zeros of Y1'(z) Y1(z1') ------------------------------------------------------------------ 1 0.576785129 0.9039847922 -0.7634970879 0.5892448647 2 -1.940477342 0.7211859189 0.1620640057 -0.9520278864 3 -5.333478617 0.5672196368 -0.0317940081 0.5968536736 4 -8.536768577 0.5560607040 0.0154177166 -0.4726011652 5 -11.706175219 0.5528590607 -0.0095443768 0.4037533396 NT= 5, KF= 0, KC= 1 No. z0, Zeros of Y0(z) Y1(z0) ------------------------------------------------------------------ 1 0.893576966 0.0000000000 -0.8794208025 0.0000000000 2 3.957678419 0.0000000000 0.4025426718 0.0000000000 3 7.086051060 0.0000000000 -0.3000976149 0.0000000000 4 10.222345043 0.0000000000 0.2497012375 0.0000000000 5 13.361097474 0.0000000000 -0.2183582966 0.0000000000 NT= 5, KF= 1, KC= 1 No. z1, Zeros of Y1(z) Y0(z1) ------------------------------------------------------------------ 1 -0.502743273 0.7862437145 -0.4595276847 1.3171019361 2 2.197141326 0.0000000000 0.5207864124 -0.0000000000 3 5.429681041 -0.0000000000 -0.3403180455 0.0000000000 4 8.596005868 -0.0000000000 0.2714598773 -0.0000000000 5 11.749154831 -0.0000000000 -0.2324617660 0.0000000000 NT= 5, KF= 2, KC= 1 No. z1', Zeros of Y1'(z) Y1(z1') ------------------------------------------------------------------ 1 -5.333478617 0.5672196368 -0.0317940081 0.5968536736 2 -1.940477342 0.7211859189 0.1620640057 -0.9520278864 3 3.683022857 -0.0000000000 0.4167299281 0.0000000000 4 6.941499954 -0.0000000000 -0.3031737401 -0.0000000000 5 10.123404655 -0.0000000000 0.2509125363 -0.0000000000 ME1XA Test E1XA x E1(x) ---------------------- 0.0 0.1000000+301 1.0 0.2193839E+00 2.0 0.4890051E-01 3.0 0.1304838E-01 4.0 0.3779352E-02 5.0 0.1148296E-02 ME1XB Test E1XB x E1(x) ------------------------- 0.0 0.1000000000+301 1.0 0.2193839344E+00 2.0 0.4890051071E-01 3.0 0.1304838109E-01 4.0 0.3779352410E-02 5.0 0.1148295591E-02 ME1Z Test E1Z z Re[E1(z)] Im[E1(z)] ----------------------------------------------- 3.0 2.0 -0.90959209D-02 -0.69001793D-02 3.0 -2.0 -0.90959209D-02 0.69001793D-02 -3.0 2.0 -0.28074891D+01 0.59603353D+01 -3.0 -2.0 -0.28074891D+01 -0.59603353D+01 25.0 10.0 -0.29302080D-12 0.40391222D-12 25.0 -10.0 -0.29302080D-12 -0.40391222D-12 -25.0 10.0 0.27279957D+10 -0.49430610D+09 -25.0 -10.0 0.27279957D+10 0.49430610D+09 MEIX Test EIX x Ei(x) ------------------------ 0.0 -0.10000000+301 1.0 0.18951178E+01 2.0 0.49542344E+01 3.0 0.99338326E+01 4.0 0.19630874E+02 5.0 0.40185275E+02 MELIT Test ELIT k phi F(k,phi) E(k,phi) --------------------------------------- 0.50 0. 0.00000000 0.00000000 0.50 15. 0.26254249 0.26106005 0.50 30. 0.52942863 0.51788193 0.50 45. 0.80436610 0.76719599 0.50 60. 1.08955067 1.00755556 0.50 75. 1.38457455 1.23988858 0.50 90. 1.68575035 1.46746221 MELIT3 Test ELIT3 Phi = 0.785398 K = 0.500000 C = 0.750000 EL3= 0.01370854 MENXA Test ENXA X = 10.0000 n En(x) ---------------------- 0 0.45399930D-05 1 0.41569689D-05 2 0.38302405D-05 3 0.35487626D-05 4 0.33041014D-05 5 0.30897289D-05 MENXB Test ENXB X = 10.0000 n En(x) ---------------------- 0 0.45399930D-05 1 0.41569689D-05 2 0.38302405D-05 3 0.35487626D-05 4 0.33041014D-05 5 0.30897289D-05 MERROR Test ERROR x erf(x) --------------------- 1.00 0.84270079 2.00 0.99532227 3.00 0.99997791 4.00 0.99999998 5.00 1.00000000 MEULERA Test EULERA n En -------------------------- 0 0.100000000000D+01 2 -0.100000000000D+01 4 0.500000000000D+01 6 -0.610000000000D+02 8 0.138500000000D+04 10 -0.505210000000D+05 MEULERB Test EULERB n En -------------------------- 0 0.100000000000D+01 2 -0.100000000000D+01 4 0.500000000000D+01 6 -0.610000000000D+02 8 0.138500000000D+04 10 -0.505210000000D+05 MFCOEF Test FCOEF m= 10, q= 5.00 Expansion coefficients of Mathieu functions n Amn(q) Bmn(q) ---------------------------------------- 0 0.16788542D-05 2 0.33619515D-04 0.33444320D-04 4 0.64298667D-03 0.64297621D-03 6 0.10784807D-01 0.10784806D-01 8 0.13767512D+00 0.13767512D+00 10 0.98395564D+00 0.98395564D+00 12 -0.11280678D+00 -0.11280678D+00 14 0.58929627D-02 0.58929627D-02 16 -0.18916571D-03 -0.18916571D-03 18 0.42264064D-05 0.42264064D-05 20 -0.70485101D-07 -0.70485101D-07 22 0.91820256D-09 0.91820256D-09 24 -0.96484263D-11 -0.96484263D-11 MFCS Test FCS x C(x) S(x) ----------------------------------- 0.0 0.00000000 0.00000000 0.5 0.49234423 0.06473243 1.0 0.77989340 0.43825915 1.5 0.44526118 0.69750496 2.0 0.48825341 0.34341568 2.5 0.45741301 0.61918176 MFCS Test FCS n Complex zeros of C(z) Complex zeros of S(z) -------------------------------------------------------- 1 1.74366749 +i 0.30573506 2.00925701 +i 0.28854790 2 2.65145960 +i 0.25290396 2.83347723 +i 0.24428524 3 3.32035934 +i 0.22395346 3.46753308 +i 0.21849268 4 3.87573449 +i 0.20474747 4.00257824 +i 0.20085103 5 4.36106352 +i 0.19066973 4.47418930 +i 0.18768859 6 4.79760774 +i 0.17970801 4.90067839 +i 0.17732036 7 5.19765324 +i 0.17081930 5.29294674 +i 0.16884418 8 5.56906016 +i 0.16339854 5.65810676 +i 0.16172492 9 5.91721728 +i 0.15706585 6.00110342 +i 0.15562108 10 6.24600976 +i 0.15156826 6.32553961 +i 0.15030246 MFFK Test FFK x Re[F+/-(x)] +/-Im[F+/-(x)] Mod[F+/-(x)] +/-Arg[F+/-(x)] -------------------------------------------------------------- 0.0 0.62665707 0.62665707 0.88622693 45.000000 x Re[K+/-(x)] +/-Im[K+/-(x)] Mod[K+/-(x)] +/-Arg[K+/-(x)] -------------------------------------------------------------- 0.0 0.50000000 0.00000000 0.50000000 0.000000 x Re[F+/-(x)] +/-Im[F+/-(x)] Mod[F+/-(x)] +/-Arg[F+/-(x)] -------------------------------------------------------------- 2.0 0.16519561 -0.17811942 0.24293233 -47.155835 x Re[K+/-(x)] +/-Im[K+/-(x)] Mod[K+/-(x)] +/-Arg[K+/-(x)] -------------------------------------------------------------- 2.0 0.10702394 0.08562295 0.13705989 38.661047 x Re[F+/-(x)] +/-Im[F+/-(x)] Mod[F+/-(x)] +/-Arg[F+/-(x)] -------------------------------------------------------------- 4.0 0.03219674 -0.12047678 0.12470479 -75.037684 x Re[K+/-(x)] +/-Im[K+/-(x)] Mod[K+/-(x)] +/-Arg[K+/-(x)] -------------------------------------------------------------- 4.0 0.05126306 0.04818949 0.07035714 43.229843 x Re[F+/-(x)] +/-Im[F+/-(x)] Mod[F+/-(x)] +/-Arg[F+/-(x)] -------------------------------------------------------------- 6.0 0.08245304 -0.01180212 0.08329342 -8.145843 x Re[K+/-(x)] +/-Im[K+/-(x)] Mod[K+/-(x)] +/-Arg[K+/-(x)] -------------------------------------------------------------- 6.0 0.03368650 0.03276566 0.04699328 44.206095 x Re[F+/-(x)] +/-Im[F+/-(x)] Mod[F+/-(x)] +/-Arg[F+/-(x)] -------------------------------------------------------------- 8.0 -0.05729996 0.02493542 0.06249048 156.482601 x Re[K+/-(x)] +/-Im[K+/-(x)] Mod[K+/-(x)] +/-Arg[K+/-(x)] -------------------------------------------------------------- 8.0 0.02512396 0.02473472 0.03525648 44.552712 x Re[F+/-(x)] +/-Im[F+/-(x)] Mod[F+/-(x)] +/-Arg[F+/-(x)] -------------------------------------------------------------- 10.0 0.02553188 0.04298617 0.04999688 59.291561 x Re[K+/-(x)] +/-Im[K+/-(x)] Mod[K+/-(x)] +/-Arg[K+/-(x)] -------------------------------------------------------------- 10.0 0.02004532 0.01984592 0.02820772 44.713609 MGAMMA Test GAMMA x (x) ---------------------------- 0.3333 0.267893853471E+01 0.5000 0.177245385091E+01 -0.5000 -0.354490770181E+01 -1.5000 0.236327180121E+01 5.0000 0.240000000000E+02 MHERZO Test HERZO n = 13 Nodes and weights for Gauss-Hermite integration i xi Wi ----------------------------------------------------- 1 0.4101337596179D+01 0.4825731850073D-07 2 0.3246608978372D+01 0.2043036040271D-04 3 0.2519735685678D+01 0.1207459992719D-02 4 0.1853107651602D+01 0.2086277529617D-01 5 0.1220055036591D+01 0.1403233206870D+00 6 0.6057638791711D+00 0.4216162968985D+00 7 0.0000000000000D+00 0.6043931879212D+00 8 -0.6057638791711D+00 0.4216162968985D+00 9 -0.1220055036591D+01 0.1403233206870D+00 10 -0.1853107651602D+01 0.2086277529617D-01 11 -0.2519735685678D+01 0.1207459992719D-02 12 -0.3246608978372D+01 0.2043036040271D-04 13 -0.4101337596179D+01 0.4825731850073D-07 MHYGFX Test HYGFX a =-2.50, b = 3.30, c = 6.70, x = 0.25F(a,b,c,x)= 0.72356129D+00 a =-2.50, b = 3.30, c = 6.70, x = 0.55F(a,b,c,x)= 0.46961432D+00 a =-2.50, b = 3.30, c = 6.70, x = 0.85F(a,b,c,x)= 0.29106096D+00 a =-0.50, b = 3.30, c = 6.70, x = 0.25F(a,b,c,x)= 0.93610145D+00 a =-0.50, b = 3.30, c = 6.70, x = 0.55F(a,b,c,x)= 0.85187390D+00 a =-0.50, b = 3.30, c = 6.70, x = 0.85F(a,b,c,x)= 0.75543187D+00 a = 0.50, b = 3.30, c = 6.70, x = 0.25F(a,b,c,x)= 0.10689695D+01 a = 0.50, b = 3.30, c = 6.70, x = 0.55F(a,b,c,x)= 0.11795358D+01 a = 0.50, b = 3.30, c = 6.70, x = 0.85F(a,b,c,x)= 0.13510497D+01 a = 2.50, b = 3.30, c = 6.70, x = 0.25F(a,b,c,x)= 0.14051563D+01 a = 2.50, b = 3.30, c = 6.70, x = 0.55F(a,b,c,x)= 0.23999063D+01 a = 2.50, b = 3.30, c = 6.70, x = 0.85F(a,b,c,x)= 0.57381566D+01 a = 3.30, b = 6.70, c =-5.50, x = 0.25F(a,b,c,x)= 0.15090670D+05 a = 3.30, b = 6.70, c =-5.50, x = 0.55F(a,b,c,x)= 0.10170778D+11 a = 3.30, b = 6.70, c =-5.50, x = 0.85F(a,b,c,x)= 0.58682088D+19 a = 3.30, b = 6.70, c =-0.50, x = 0.25F(a,b,c,x)= -0.21631479D+04 a = 3.30, b = 6.70, c =-0.50, x = 0.55F(a,b,c,x)= -0.30854772D+07 a = 3.30, b = 6.70, c =-0.50, x = 0.85F(a,b,c,x)= -0.10217370D+13 a = 3.30, b = 6.70, c = 0.50, x = 0.25F(a,b,c,x)= 0.26451677D+03 a = 3.30, b = 6.70, c = 0.50, x = 0.55F(a,b,c,x)= 0.11967860D+06 a = 3.30, b = 6.70, c = 0.50, x = 0.85F(a,b,c,x)= 0.92370648D+10 a = 3.30, b = 6.70, c = 4.50, x = 0.25F(a,b,c,x)= 0.41946916D+01 a = 3.30, b = 6.70, c = 4.50, x = 0.55F(a,b,c,x)= 0.58092729D+02 a = 3.30, b = 6.70, c = 4.50, x = 0.85F(a,b,c,x)= 0.20396914D+05 MHYGFZ Test HYGFZ a b c x y Re[F] Im[F] ------------------------------------------------------------------- HYGFZ - Warning! The solution returned may have low accuracy. 3.2 1.8 6.7 1.0 0.0 0.54689992D+01 0.00000000D+00 HYGFZ - Warning! The solution returned may have low accuracy. 3.2 -1.8 6.7 1.0 0.0 0.33750635D+00 0.00000000D+00 -5.0 3.3 6.7 5.2 4.8 0.11682750D+03 0.60389096D+03 3.3 -6.0 3.7 5.2 -4.8 0.17620418D+05 0.38293809D+05 -7.0 3.3 -3.7 5.2 -4.8 -0.11772775D+11 -0.14382286D+11 4.3 -8.0 -3.7 5.2 4.8 0.13161186D+13 -0.10129889D+12 3.3 5.8 6.7 0.2 0.1 0.17330557D+01 0.63401029D+00 3.5 -2.4 6.7 0.2 0.5 0.64762241D+00 -0.52110507D+00 HYGFZ - Warning! The solution returned may have low accuracy. 3.3 4.3 6.7 0.8 0.3 -0.14830083D+01 0.83744262D+01 7.0 5.0 4.1 3.0 -1.0 -0.40376095D-02 -0.29566326D-02 5.0 7.0 4.1 3.0 -1.0 -0.40376095D-02 -0.29566326D-02 3.5 1.2 9.7 0.6 0.9 0.10343044D+01 0.54473814D+00 HYGFZ - Warning! The solution returned may have low accuracy. 2.1 5.4 9.7 0.5 0.7 0.68850440D+00 0.12274187D+01 HYGFZ - Warning! The solution returned may have low accuracy. 8.7 3.2 6.7 0.5 0.7 -0.90046497D+00 -0.11198899D+01 HYGFZ - Warning! The solution returned may have low accuracy. 8.7 2.7 6.7 0.5 0.9 -0.44405252D+02 0.25663088D+02 MIK01A Test IK01A x I0(x) I0'(x) I1(x) I1'(x) ----------------------------------------------------------------- 1.0 0.1266066D+01 0.5651591D+00 0.5651591D+00 0.7009068D+00 10.0 0.2815717D+04 0.2670988D+04 0.2670988D+04 0.2548618D+04 20.0 0.4355828D+08 0.4245497D+08 0.4245497D+08 0.4143553D+08 30.0 0.7816723D+12 0.7685320D+12 0.7685320D+12 0.7560546D+12 40.0 0.1489477D+17 0.1470740D+17 0.1470740D+17 0.1452709D+17 50.0 0.2932554D+21 0.2903079D+21 0.2903079D+21 0.2874492D+21 x K0(x) K0'(x) K1(x) K1'(x) ----------------------------------------------------------------- 1.0 0.4210244D+00 -0.6019072D+00 0.6019072D+00 -0.1022932D+01 10.0 0.1778006D-04 -0.1864877D-04 0.1864877D-04 -0.1964494D-04 20.0 0.5741238D-09 -0.5883058D-09 0.5883058D-09 -0.6035391D-09 30.0 0.2132477D-13 -0.2167732D-13 0.2167732D-13 -0.2204735D-13 40.0 0.8392861D-18 -0.8497132D-18 0.8497132D-18 -0.8605289D-18 50.0 0.3410168D-22 -0.3444102D-22 0.3444102D-22 -0.3479050D-22 MIK01B Test IK01B x I0(x) I0'(x) I1(x) I1'(x) ----------------------------------------------------------------- 1.0 0.1266066D+01 0.5651591D+00 0.5651591D+00 0.7009068D+00 10.0 0.2815717D+04 0.2670988D+04 0.2670988D+04 0.2548618D+04 20.0 0.4355829D+08 0.4245497D+08 0.4245497D+08 0.4143554D+08 30.0 0.7816723D+12 0.7685320D+12 0.7685320D+12 0.7560546D+12 40.0 0.1489477D+17 0.1470740D+17 0.1470740D+17 0.1452709D+17 50.0 0.2932553D+21 0.2903080D+21 0.2903080D+21 0.2874491D+21 x K0(x) K0'(x) K1(x) K1'(x) ----------------------------------------------------------------- 1.0 0.4210244D+00 -0.6019072D+00 0.6019072D+00 -0.1022932D+01 10.0 0.1778006D-04 -0.1864877D-04 0.1864877D-04 -0.1964494D-04 20.0 0.5741238D-09 -0.5883057D-09 0.5883057D-09 -0.6035391D-09 30.0 0.2132478D-13 -0.2167732D-13 0.2167732D-13 -0.2204736D-13 40.0 0.8392862D-18 -0.8497131D-18 0.8497131D-18 -0.8605291D-18 50.0 0.3410168D-22 -0.3444102D-22 0.3444102D-22 -0.3479050D-22 MIKNA Test IKNA n In(x) In'(x) Kn(x) Kn'(x) --------------------------------------------------------------- 0 0.2815717D+04 0.2670988D+04 0.1778006D-04 -0.1864877D-04 1 0.2670988D+04 0.2548618D+04 0.1864877D-04 -0.1964494D-04 2 0.2281519D+04 0.2214685D+04 0.2150982D-04 -0.2295074D-04 3 0.1758381D+04 0.1754005D+04 0.2725270D-04 -0.2968563D-04 4 0.1226491D+04 0.1267785D+04 0.3786144D-04 -0.4239728D-04 5 0.7771883D+03 0.8378964D+03 0.5754185D-04 -0.6663236D-04 MIKNB Test IKNB n In(x) In'(x) Kn(x) Kn'(x) --------------------------------------------------------------- 0 0.2815717D+04 0.2670988D+04 0.1778006D-04 -0.1864877D-04 1 0.2670988D+04 0.2548618D+04 0.1864877D-04 -0.1964494D-04 2 0.2281519D+04 0.2214685D+04 0.2150982D-04 -0.2295074D-04 3 0.1758381D+04 0.1754005D+04 0.2725270D-04 -0.2968563D-04 4 0.1226491D+04 0.1267785D+04 0.3786144D-04 -0.4239728D-04 5 0.7771883D+03 0.8378964D+03 0.5754185D-04 -0.6663236D-04 MIKV Test IKV v = n+v0, v0 =0.25000, x = 10.0 n Iv(x) Iv'(x) Kv(x) Kv'(x) --------------------------------------------------------------------- 0 0.28064359D+04 0.26631677D+04 0.17833184D-04 -0.18709581D-04 1 0.25930068D+04 0.24823101D+04 0.19155411D-04 -0.20227611D-04 2 0.21581842D+04 0.21074153D+04 0.22622037D-04 -0.24245369D-04 3 0.16218239D+04 0.16310915D+04 0.29335327D-04 -0.32156018D-04 4 0.11039987D+04 0.11526244D+04 0.41690000D-04 -0.47053577D-04 5 0.68342498D+03 0.74520058D+03 0.64771827D-04 -0.75695209D-04 MINCOB Test INCOB a b x Ix(a,b) ----------------------------------- 1.0 3.0 0.25 0.57812500 MINCOG Test INCOG a x r(a,x) (a,x) P(a,x) -------------------------------------------------------- 3.0 0.2 0.43229934D-02 0.19956770D+01 0.21614967D-02 MITAIRY Test ITAIRY x Ai(t)dt Bi(t)dt Ai(-t)dt Bi(-t)dt ---------------------------------------------------------------- 5.0 0.33328759 0.32147832D+03 0.71788220 0.15873094 10.0 0.33333333 0.14780980D+09 0.76569840 0.01504042 15.0 0.33333333 0.49673090D+16 0.68358063 0.07202621 20.0 0.33333333 0.47447423D+25 0.71173925 -0.03906173 25.0 0.33333333 0.78920820D+35 0.70489539 0.03293190 MITIKA Test ITIKA x I0(t)dt K0(t)dt -------------------------------------- 5.0 0.31848668D+02 1.56738739 10.0 0.29930445D+04 1.57077931 15.0 0.35262048D+06 1.57079623 20.0 0.44758593D+08 1.57079633 25.0 0.58991731D+10 1.57079633 MITIKB Test ITIKB x I0(t)dt K0(t)dt -------------------------------------- 5.0 0.318487D+02 1.567387 10.0 0.299305D+04 1.570779 15.0 0.352619D+06 1.570796 20.0 0.447586D+08 1.570796 25.0 0.589919D+10 1.570796 MITJYA Test ITJYA x J0(t)dt Y0(t)dt --------------------------------------- 5.0 0.71531192 0.19971939 10.0 1.06701130 0.24129032 15.0 1.20516194 0.00745772 20.0 1.05837882 -0.16821597 25.0 0.87101492 -0.09360793 30.0 0.88424909 0.08822971 MITJYB Test ITJYB x J0(t)dt Y0(t)dt --------------------------------------- 5.0 0.71531192 0.19971938 10.0 1.06701130 0.24129032 15.0 1.20516194 0.00745772 20.0 1.05837882 -0.16821598 25.0 0.87101492 -0.09360793 30.0 0.88424909 0.08822971 MITSH0 Test ITSH0 x H0(t)dt ---------------------- 0.0 0.0000000E+00 5.0 0.2044244E+01 10.0 0.2518958E+01 15.0 0.2541582E+01 20.0 0.2548452E+01 25.0 0.2764836E+01 30.0 0.3062572E+01 35.0 0.3198506E+01 40.0 0.3148418E+01 45.0 0.3116223E+01 50.0 0.3244522E+01 MITSL0 Test ITSL0 x L0(t)dt ----------------------- 0.0 0.0000000D+00 5.0 0.3003079D+02 10.0 0.2990773D+04 15.0 0.3526179D+06 20.0 0.4475860D+08 25.0 0.5899173D+10 30.0 0.7955389D+12 35.0 0.1089556D+15 40.0 0.1508972D+17 45.0 0.2107523D+19 50.0 0.2962966D+21 MITTH0 Test ITTH0 x H0(t)/t dt ----------------------- 0.0 0.15707963E+01 5.0 0.79545751E-01 10.0 0.40471751E-01 15.0 0.42765583E-01 20.0 0.40307959E-01 25.0 0.28977663E-01 30.0 0.18152557E-01 35.0 0.14627026E-01 40.0 0.16213313E-01 45.0 0.16733600E-01 50.0 0.13786606E-01 MITTIKA Test ITTIKA x [1-I0(t)]/tdt K0(t)/tdt --------------------------------------- 5.0 0.71047763D+01 0.58635626D-03 10.0 0.34081537D+03 0.15629282D-05 15.0 0.25437619D+05 0.59837472D-08 20.0 0.23673661D+07 0.26790545D-10 25.0 0.24652751D+09 0.13100706D-12 MITTIKB Test ITTIKB x [1-I0(t)]/tdt K0(t)/tdt --------------------------------------- 5.0 0.710478D+01 0.586361D-03 10.0 0.340811D+03 0.156293D-05 15.0 0.254373D+05 0.598363D-08 20.0 0.236735D+07 0.267906D-10 25.0 0.246534D+09 0.131007D-12 MITTJYA Test ITTJYA x [1-J0(t)]/tdt Y0(t)/tdt ------------------------------------------- 5.0 0.15403472D+01 -0.46322055D-01 10.0 0.21778664D+01 -0.22987934D-01 15.0 0.25785507D+01 0.38573574D-03 20.0 0.28773106D+01 0.85031527D-02 25.0 0.31082313D+01 0.35263393D-02 30.0 0.32890167D+01 -0.30602912D-02 MITTJYB Test ITTJYB x [1-J0(t)]/tdt Y0(t)/tdt ---------------------------------------- 5.0 0.1540347D+01 -0.4632208D-01 10.0 0.2177866D+01 -0.2298791D-01 15.0 0.2578551D+01 0.3857453D-03 20.0 0.2877311D+01 0.8503154D-02 25.0 0.3108231D+01 0.3526339D-02 MJDZO Test JDZO Total number of the zeros: 9 Table Zeros of Bessel functions Jn(x) and Jn'(x) -------------------------------------------------------------------- 1 TE 1 - 1 1.84118378 | 2 TM 0 - 1 2.40482556 | 3 TE 2 - 1 3.05423693 | 4 TM 1 - 1 3.83170597 | 5 TE 0 - 1 3.83170597 | 6 TE 3 - 1 4.20118894 | 7 TM 2 - 1 5.13562230 | 8 TE 4 - 1 5.31755313 | 9 TE 1 - 2 5.33144277 | -------------------------------------------------------------------- MJELP Test JELP k u phi sn u cn u dn u ---------------------------------------------------------------- 0.500 0.0000000 0.00000 0.0000000 1.0000000 1.0000000 0.500 0.5000000 28.36475 0.4750829 0.8799410 0.9713774 0.500 1.0000000 55.34950 0.8226356 0.5685690 0.9114920 0.500 1.5000000 80.76995 0.9870523 0.1603988 0.8697310 0.500 2.0000000 105.65623 0.9628982 -0.2698650 0.8764741 MJY01A Test JY01A x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 1.0 0.76519769E+00 -0.44005059E+00 0.44005059E+00 0.32514710E+00 1.0 0.88256964E-01 0.78121282E+00 -0.78121282E+00 0.86946979E+00 5.0 -0.17759677E+00 0.32757914E+00 -0.32757914E+00 -0.11208094E+00 5.0 -0.30851763E+00 -0.14786314E+00 0.14786314E+00 -0.33809025E+00 10.0 -0.24593576E+00 -0.43472746E-01 0.43472746E-01 -0.25028304E+00 10.0 0.55671167E-01 -0.24901542E+00 0.24901542E+00 0.30769625E-01 20.0 0.16702466E+00 -0.66833124E-01 0.66833124E-01 0.16368301E+00 20.0 0.62640597E-01 0.16551161E+00 -0.16551161E+00 0.70916178E-01 30.0 -0.86367984E-01 0.11875106E+00 -0.11875106E+00 -0.82409615E-01 30.0 -0.11729573E+00 -0.84425571E-01 0.84425571E-01 -0.12010992E+00 40.0 0.73668906E-02 -0.12603832E+00 0.12603832E+00 0.42159326E-02 40.0 0.12593642E+00 0.57935058E-02 -0.57935058E-02 0.12608125E+00 50.0 0.55812328E-01 0.97511828E-01 -0.97511828E-01 0.57762564E-01 50.0 -0.98064995E-01 0.56795669E-01 -0.56795669E-01 -0.96929082E-01 MJY01B Test JY01B x J0(x) J0'(x) J1(x) J1'(x) ---------------------------------------------------------------------- 1.0 0.76519769E+00 -0.44005059E+00 0.44005059E+00 0.32514710E+00 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 1.0 0.88256964E-01 0.78121282E+00 -0.78121282E+00 0.86946979E+00 5.0 -0.17759677E+00 0.32757914E+00 -0.32757914E+00 -0.11208094E+00 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 5.0 -0.30851763E+00 -0.14786314E+00 0.14786314E+00 -0.33809025E+00 10.0 -0.24593576E+00 -0.43472746E-01 0.43472746E-01 -0.25028304E+00 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 10.0 0.55671167E-01 -0.24901542E+00 0.24901542E+00 0.30769625E-01 20.0 0.16702466E+00 -0.66833124E-01 0.66833124E-01 0.16368301E+00 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 20.0 0.62640597E-01 0.16551161E+00 -0.16551161E+00 0.70916178E-01 30.0 -0.86367984E-01 0.11875106E+00 -0.11875106E+00 -0.82409615E-01 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 30.0 -0.11729573E+00 -0.84425571E-01 0.84425571E-01 -0.12010992E+00 40.0 0.73668905E-02 -0.12603832E+00 0.12603832E+00 0.42159326E-02 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 40.0 0.12593642E+00 0.57935059E-02 -0.57935059E-02 0.12608125E+00 50.0 0.55812328E-01 0.97511828E-01 -0.97511828E-01 0.57762564E-01 x Y0(x) Y0'(x) Y1(x) Y1'(x) ---------------------------------------------------------------------- 50.0 -0.98064995E-01 0.56795669E-01 -0.56795669E-01 -0.96929082E-01 MJYNA Test JYNA n Jn(x) Jn'(x) Yn(x) Yn'(x) -------------------------------------------------------------- 0 -0.2459358D+00 -0.4347275D-01 0.5567117D-01 -0.2490154D+00 10 0.2074861D+00 0.8436958D-01 -0.3598142D+00 0.1605149D+00 20 0.1151337D-04 0.2011954D-04 -0.1597484D+04 0.2737803D+04 30 0.1551096D-11 0.4396479D-11 -0.7256142D+10 0.2047617D+11 MJYNB Test JYNB n Jn(x) Jn'(x) Yn(x) Yn'(x) -------------------------------------------------------------- 0 -0.2459358D+00 -0.4347275D-01 0.5567117D-01 -0.2490154D+00 10 0.2074861D+00 0.8436958D-01 -0.3598142D+00 0.1605149D+00 20 0.1151337D-04 0.2011954D-04 -0.1597484D+04 0.2737803D+04 30 0.1551096D-11 0.4396479D-11 -0.7256142D+10 0.2047617D+11 MJYV Test JYV v Jv(x) Jv'(x) Yv(x) Yv'(x) --------------------------------------------------------------------- 0.25 -0.20639379D+00 -0.13476340D+00 0.14493044D+00 -0.21381777D+00 1.25 0.12960355D+00 -0.22259423D+00 0.21744103D+00 0.11775031D+00 2.25 0.23879467D+00 0.75874750D-01 -0.90570182D-01 0.23781932D+00 3.25 -0.22145948D-01 0.24599211D+00 -0.25819761D+00 -0.66559577D-02 4.25 -0.25318954D+00 0.85459607D-01 -0.77258266D-01 -0.22536285D+00 5.25 -0.19306516D+00 -0.15183033D+00 0.19252809D+00 -0.17833551D+00 MJYZO Test JYZO Zeros of Bessel funcions Jn(x), Yn(x) and their derivatives ( n = 1 ) m jnm j'nm ynm y'nm ----------------------------------------------------------- 1 3.8317060 1.8411838 2.1971413 3.6830229 2 7.0155867 5.3314428 5.4296810 6.9415000 3 10.1734681 8.5363164 8.5960059 10.1234047 4 13.3236919 11.7060049 11.7491548 13.2857582 5 16.4706301 14.8635886 14.8974421 16.4400580 MKLVNA Test KLVNA x ber x bei x ker x kei x ---------------------------------------------------------------------- 0.0 0.10000000D+01 0.00000000D+00 0.10000000+301 -0.78539816D+00 5.0 -0.62300825D+01 0.11603438D+00 -0.11511727D-01 0.11187587D-01 10.0 0.13884047D+03 0.56370459D+02 0.12946633D-03 -0.30752457D-03 15.0 -0.29672545D+04 -0.29527079D+04 -0.15143472D-07 0.79628944D-05 20.0 0.47489370D+05 0.11477520D+06 -0.77152331D-07 -0.18589415D-06 x ber'x bei'x ker'x kei'x ---------------------------------------------------------------------- 0.0 0.00000000D+00 0.00000000D+00 -0.10000000+301 0.00000000D+00 5.0 -0.38453395D+01 -0.43541405D+01 0.17193404D-01 -0.81998654D-03 10.0 0.51195258D+02 0.13530930D+03 -0.31559693D-03 0.14091384D-03 15.0 0.91055333D+02 -0.40877552D+04 0.56446781D-05 -0.58822228D-05 20.0 -0.48803198D+05 0.11185503D+06 -0.75018592D-07 0.19062428D-06 MKLVNB Test KLVNB x ber x bei x ker x kei x ---------------------------------------------------------------------- 0.0 0.100000D+01 0.000000D+00 0.100000+301 -0.785398D+00 x ber'x bei'x ker'x kei'x ---------------------------------------------------------------------- 0.0 0.000000D+00 0.000000D+00 -0.100000+301 0.000000D+00 5.0 -0.623008D+01 0.116034D+00 -0.115117D-01 0.111876D-01 x ber'x bei'x ker'x kei'x ---------------------------------------------------------------------- 5.0 -0.384534D+01 -0.435414D+01 0.171934D-01 -0.819979D-03 10.0 0.138840D+03 0.563705D+02 0.129466D-03 -0.307525D-03 x ber'x bei'x ker'x kei'x ---------------------------------------------------------------------- 10.0 0.511952D+02 0.135309D+03 -0.315597D-03 0.140914D-03 15.0 -0.296725D+04 -0.295271D+04 -0.151433D-07 0.796289D-05 x ber'x bei'x ker'x kei'x ---------------------------------------------------------------------- 15.0 0.910555D+02 -0.408776D+04 0.564468D-05 -0.588222D-05 20.0 0.474894D+05 0.114775D+06 -0.771523D-07 -0.185894D-06 x ber'x bei'x ker'x kei'x ---------------------------------------------------------------------- 20.0 -0.488032D+05 0.111855D+06 -0.750186D-07 0.190624D-06 MKLVNZO Test KLVNZO m ber x bei x ker x kei x --------------------------------------------------------------- 1 2.84891782 5.02622395 1.71854296 3.91466761 2 7.23882945 9.45540630 6.12727913 8.34422506 3 11.67396355 13.89348785 10.56294271 12.78255715 4 16.11356383 18.33398346 15.00268812 17.22314372 5 20.55463158 22.77543929 19.44381663 21.66464214 Zeros of Kelvin functions ber'x, bei'x, ker'x and kei'x m ber'x bei'x ker'x kei'x --------------------------------------------------------------- 1 6.03871081 3.77267330 2.66583979 4.93181194 2 10.51364251 8.28098785 7.17212212 9.40405458 3 14.96844542 12.74214752 11.63218639 13.85826916 4 19.41757493 17.19343175 16.08312025 18.30717294 5 23.86430432 21.64114394 20.53067845 22.75379258 MLAGZO Test LAGZO Nodes and weights for Gauss-Lagurre integration i xi Wi ----------------------------------------------------- 1 0.1523222277318D+00 0.3361264217980D+00 2 0.8072200227423D+00 0.4112139804240D+00 3 0.2005135155619D+01 0.1992875253709D+00 4 0.3783473973331D+01 0.4746056276565D-01 5 0.6204956777877D+01 0.5599626610795D-02 6 0.9372985251688D+01 0.3052497670932D-03 7 0.1346623691109D+02 0.6592123026075D-05 8 0.1883359778899D+02 0.4110769330350D-07 9 0.2637407189093D+02 0.3290874030351D-10 MLEGZO Test LEGZO Nodes and weights for Gauss-Legendre integration i xi Wi ------------------------------------------------ 1 0.9681602395076 0.8127438836157D-01 2 0.8360311073266 0.1806481606949D+00 3 0.6133714327006 0.2606106964029D+00 4 0.3242534234038 0.3123470770400D+00 5 -0.0000000000000 0.3302393550013D+00 6 -0.3242534234038 0.3123470770400D+00 7 -0.6133714327006 0.2606106964029D+00 8 -0.8360311073266 0.1806481606949D+00 9 -0.9681602395076 0.8127438836157D-01 MLGAMA Test LGAMA x (x) ------------------------- 0.5 0.1772453851D+01 2.5 0.1329340388D+01 5.0 0.2400000000D+02 7.5 0.1871254306D+04 10.0 0.3628800000D+06 MLAMN Test LAMN n lambda(x) lambda'(x) --------------------------------------- 0 -0.24593576D+00 -0.43472746D-01 1 0.86945492D-02 -0.50926063D-01 2 0.20370425D-01 -0.46703503D-02 3 0.28022102D-02 0.10540929D-01 4 -0.84327431D-02 0.89879627D-02 5 -0.89879627D-02 0.55521954D-03 MLAMV Test LAMV v Lambda(x) Lambda'(x) ------------------------------------------- 0.75 -0.13657787D-01 -0.66234027D-01 1.75 0.23181910D-01 -0.12893894D-01 0.00 -0.24593576D+00 -0.43472746D-01 1.00 0.86945492D-02 -0.50926063D-01 2.00 0.20370425D-01 -0.46703503D-02 0.25 -0.12510515D+00 -0.78558916D-01 1.25 0.19639729D-01 -0.36186221D-01 2.25 0.16283799D-01 0.15101684D-02 0.50 -0.54402111D-01 -0.78466942D-01 1.50 0.23540083D-01 -0.23382658D-01 2.50 0.11691329D-01 0.59243767D-02 MLPMN Test LPMN m n x Pmn(x) Pmn'(x) --------------------------------------------------- 0 0 0.5 0.10000000E+01 0.00000000E+00 0 1 0.5 0.50000000E+00 0.10000000E+01 0 2 0.5 -0.12500000E+00 0.15000000E+01 0 3 0.5 -0.43750000E+00 0.37500000E+00 0 4 0.5 -0.28906250E+00 -0.15625000E+01 1 0 0.5 0.00000000E+00 0.00000000E+00 1 1 0.5 -0.86602540E+00 0.57735027E+00 1 2 0.5 -0.12990381E+01 -0.17320508E+01 1 3 0.5 -0.32475953E+00 -0.62786842E+01 1 4 0.5 0.13531647E+01 -0.57735027E+01 2 0 0.5 0.00000000E+00 0.00000000E+00 2 1 0.5 0.00000000E+00 0.00000000E+00 2 2 0.5 0.22500000E+01 -0.30000000E+01 2 3 0.5 0.56250000E+01 0.37500000E+01 2 4 0.5 0.42187500E+01 0.33750000E+02 3 0 0.5 0.00000000E+00 0.00000000E+00 3 1 0.5 0.00000000E+00 0.00000000E+00 3 2 0.5 0.00000000E+00 0.00000000E+00 3 3 0.5 -0.97427858E+01 0.19485572E+02 3 4 0.5 -0.34099750E+02 0.14210855E-13 4 0 0.5 0.00000000E+00 0.00000000E+00 4 1 0.5 0.00000000E+00 0.00000000E+00 4 2 0.5 0.00000000E+00 0.00000000E+00 4 3 0.5 0.00000000E+00 0.00000000E+00 4 4 0.5 0.59062500E+02 -0.15750000E+03 MLPMNS Test LPMNS n Pmn(x) Pmn'(x) ------------------------------------- 0 0.00000000D+00 -0.00000000D+00 1 0.86602540D+00 -0.57735027D+00 2 0.12990381D+01 0.17320508D+01 3 0.32475953D+00 0.62786842D+01 4 -0.13531647D+01 0.57735027D+01 5 -0.19282597D+01 -0.43977853D+01 0 0.00000000D+00 -0.00000000D+00 1 0.00000000D+00 0.00000000D+00 2 0.15750000D+02 0.15000000D+02 3 0.19687500D+03 0.26625000D+03 4 0.16832812D+04 0.29812500D+04 5 0.12230859D+05 0.26876719D+05 6 0.81141416D+05 0.21319512D+06 MLPMN Test LPMN v Pmv(x) ----------------------- 1.5 0.46218726E+00 1.6 0.48103143E+00 1.7 0.45031429E+00 1.8 0.36216902E+00 1.9 0.21206446E+00 2.0 -0.00000000E+00 2.5 -0.15199623E+01 MLPN Test LPN n Pn(x) Pn'(x) --------------------------------------- 0 0.10000000E+01 0.00000000E+00 1 0.50000000E+00 0.10000000E+01 2 -0.12500000E+00 0.15000000E+01 3 -0.43750000E+00 0.37500000E+00 4 -0.28906250E+00 -0.15625000E+01 5 0.89843750E-01 -0.22265625E+01 MLPNI Test LPNI n Pn(x) Pn'(x) Pn(t)dt --------------------------------------------------- 0 0.10000000E+01 0.00000000E+00 0.50000000E+00 1 0.50000000E+00 0.10000000E+01 0.12500000E+00 2 -0.12500000E+00 0.15000000E+01 -0.18750000E+00 3 -0.43750000E+00 0.37500000E+00 -0.14843750E+00 4 -0.28906250E+00 -0.15625000E+01 0.58593750E-01 5 0.89843750E-01 -0.22265625E+01 0.11816406E+00 MLQMN Test LQMN m n x Qmn(x) Qmn'(x) --------------------------------------------------- 0 0 0.5 0.54930614D+00 0.13333333D+01 0 1 0.5 -0.72534693D+00 0.12159728D+01 0 2 0.5 -0.81866327D+00 -0.84270745D+00 0 3 0.5 -0.19865477D+00 -0.28773435D+01 0 4 0.5 0.44017453D+00 -0.22332909D+01 1 0 0.5 -0.11547005D+01 -0.76980036D+00 1 1 0.5 -0.10530633D+01 -0.23771592D+01 1 2 0.5 0.72980606D+00 -0.51853281D+01 1 3 0.5 0.24918526D+01 -0.10914062D+01 1 4 0.5 0.19340866D+01 0.11454786D+02 2 0 0.5 0.13333333D+01 0.44444444D+01 2 1 0.5 0.26666667D+01 0.35555556D+01 2 2 0.5 0.40692722D+01 0.87965260D+01 2 3 0.5 -0.49348627D+00 0.28115454D+02 2 4 0.5 -0.11036781D+02 0.25483527D+02 3 0 0.5 -0.53886025D+01 -0.20014809D+02 3 1 0.5 -0.61584029D+01 -0.24633611D+02 3 2 0.5 -0.12316806D+02 -0.24633611D+02 3 3 0.5 -0.23778868D+02 -0.50976710D+02 3 4 0.5 -0.93252042D+01 -0.19706889D+03 4 0 0.5 0.26666667D+02 0.14577778D+03 4 1 0.5 0.32000000D+02 0.15644444D+03 4 2 0.5 0.42666667D+02 0.19911111D+03 4 3 0.5 0.85333333D+02 0.22755556D+03 4 4 0.5 0.18681839D+03 0.41203984D+03 0 0 2.0 0.54930614D+00 -0.33333333D+00 0 1 2.0 0.98612289D-01 -0.11736052D+00 0 2 2.0 0.21183794D-01 -0.37496467D-01 0 3 2.0 0.48711203D-02 -0.11441553D-01 0 4 2.0 0.11610758D-02 -0.33986249D-02 1 0 2.0 -0.57735027D+00 0.38490018D+00 1 1 2.0 -0.20327439D+00 0.24938392D+00 1 2 2.0 -0.64945787D-01 0.11668001D+00 1 3 2.0 -0.19817351D-01 0.46959679D-01 1 4 2.0 -0.58865910D-02 0.17331343D-01 2 0 2.0 0.13333333D+01 -0.11111111D+01 2 1 2.0 0.66666667D+00 -0.88888889D+00 2 2 2.0 0.27708863D+00 -0.51943738D+00 2 3 2.0 0.10421966D+00 -0.25337507D+00 2 4 2.0 0.36816016D-01 -0.11026327D+00 3 0 2.0 -0.50037023D+01 0.53886025D+01 3 1 2.0 -0.30792014D+01 0.46188022D+01 3 2 2.0 -0.15396007D+01 0.30792014D+01 3 3 2.0 -0.67954349D+00 0.17201145D+01 3 4 2.0 -0.27600453D+00 0.84958938D+00 4 0 2.0 0.26666667D+02 -0.36444444D+02 4 1 2.0 0.18666667D+02 -0.32000000D+02 4 2 2.0 0.10666667D+02 -0.23111111D+02 4 3 2.0 0.53333333D+01 -0.14222222D+02 4 4 2.0 0.24276397D+01 -0.77485163D+01 MLQMNS Test LQMNS n Qmn(x) Qmn'(x) ------------------------------------- m = 1, n = 5, x = 0.5 0 0.11547005D+01 0.76980036D+00 1 0.10530633D+01 0.23771592D+01 2 -0.72980606D+00 0.51853281D+01 3 -0.24918526D+01 0.10914062D+01 4 -0.19340866D+01 -0.11454786D+02 5 0.93896830D+00 -0.18602587D+02 m = 2, n = 5, x = 2.5 0 0.95238095D+00 -0.52607710D+00 1 0.38095238D+00 -0.36281179D+00 2 0.12485160D+00 -0.17134314D+00 3 0.36835513D-01 -0.66284127D-01 4 0.10181730D-01 -0.22703958D-01 5 0.26919481D-02 -0.71662396D-02 MLQNA Test LQNA n Qn(x) Qn'(x) --------------------------------- 0 0.54930614 1.33333333 1 -0.72534693 1.21597281 2 -0.81866327 -0.84270745 3 -0.19865477 -2.87734353 4 0.44017453 -2.23329085 5 0.55508089 1.08422720 MLQNB Test LQNB n x Qn(x) Qn'(x) ------------------------------------------- 0 0.50000 0.54930614 1.33333333 1 0.50000 -0.72534693 1.21597281 2 0.50000 -0.81866327 -0.84270745 3 0.50000 -0.19865477 -2.87734353 4 0.50000 0.44017453 -2.23329085 5 0.50000 0.55508089 1.08422720 n x Qn(x) Qn'(x) ------------------------------------------- 0 2.50000 0.42364893D+00 -0.19047619D+00 1 2.50000 0.59122325D-01 -0.52541546D-01 2 2.50000 0.98842555D-02 -0.13109214D-01 3 2.50000 0.17695141D-02 -0.31202687D-02 4 2.50000 0.32843271D-03 -0.72261513D-03 5 2.50000 0.62335892D-04 -0.16437427D-03 MMTU0 Test MTU0 m q x cem(x,q) cem'(x,q) sem(x,q) sem'(x,q) ---------------------------------------------------------------------------- 0 5.00 40.0 0.302568280 0.947024699 0.055957488 3.119282352 1 5.00 40.0 0.766965228 1.287309746 0.298805184 0.960682376 2 5.00 40.0 -0.764052130 29.641188401 0.754926377 1.474312832 5 5.00 40.0 -0.981093138 -0.632857586 0.169484981 -4.867645502 0 25.00 40.0 0.051537120 0.382373744 -0.139807793 2.520192254 1 25.00 40.0 0.207440271 1.264630079 0.051536503 0.382377727 2 25.00 40.0 0.529705047 2.429267868 0.207427513 1.264699605 5 25.00 40.0 0.750715922 -3.904701223 1.188123243 0.325808111 MMTU12 Test MTU12 x Mcm(1)(x,q) Mcm(1)'(x,q) Mcm(2)(x,q) Mcm(2)'(x,q) --------------------------------------------------------------------- 40.0 0.69532381-309 -0.60447737D+01 0.18011172-307 -0.92469675-290 WRONSKIAN= 0.10887346-306 should equal 2/PI= 0.63661977E+00 Caution: This check is not accurate if it involves the subtraction of two similar numbers x Msm(1)(x,q) Msm(1)'(x,q) Msm(2)(x,q) Msm(2)'(x,q) --------------------------------------------------------------------- 40.0 0.81488230D+31 -0.24446469D+32 0.37000535D-47 0.67437461D-56 WRONSKIAN= 0.90453244E-16 should equal 2/PI= 0.63661977E+00 Caution: This check is not accurate if it involves the subtraction of two similar numbers MPSI Test PSI n Tn(x) Tn'(x) ----------------------------------------- 0 0.10000000D+01 0.00000000D+00 1 0.25000000D+00 0.10000000D+01 2 -0.87500000D+00 0.10000000D+01 3 -0.68750000D+00 -0.22500000D+01 4 0.53125000D+00 -0.35000000D+01 5 0.95312500D+00 0.15625000D+01 n Un(x) Un'(x) ----------------------------------------- 0 0.10000000D+01 0.00000000D+00 1 0.50000000D+00 0.20000000D+01 2 -0.75000000D+00 0.20000000D+01 3 -0.87500000D+00 -0.25000000D+01 4 0.31250000D+00 -0.50000000D+01 5 0.10312500D+01 0.62500000D+00 n Ln(x) Ln'(x) ----------------------------------------- 0 0.10000000D+01 0.00000000D+00 1 0.75000000D+00 -0.10000000D+01 2 0.53125000D+00 -0.17500000D+01 3 0.34114583D+00 -0.22812500D+01 4 0.17724609D+00 -0.26223958D+01 5 0.37263997D-01 -0.27996419D+01 n Hn(x) Hn'(x) ----------------------------------------- 0 0.10000000D+01 0.00000000D+00 1 0.50000000D+00 0.20000000D+01 2 -0.17500000D+01 0.20000000D+01 3 -0.28750000D+01 -0.10500000D+02 4 0.90625000D+01 -0.23000000D+02 5 0.27531250D+02 0.90625000D+02 MPBDV Test PBDV v Dv(x) Dv'(x) --------------------------------------- 0.5 0.43971930D-10 -0.21767183D-09 1.5 0.43753148D-09 -0.21216995D-08 2.5 0.43093569D-08 -0.20452956D-07 3.5 0.41999741D-07 -0.19491595D-06 4.5 0.40491466D-06 -0.18355745D-05 5.5 0.38601477D-05 -0.17073708D-04 v = 5.5, Dv(x)=0.38601477D-05, Dv'(x)=-.17073708D-04 MPBVV Test PBVV v Vv(x) Vv'(x) --------------------------------------- 0.5 0.18522719D+10 0.89761157D+10 1.5 0.19016268D+09 0.90145854D+09 2.5 0.19741946D+08 0.91452949D+08 3.5 0.20733667D+07 0.93751130D+07 4.5 0.22038231D+06 0.97145511D+06 5.5 0.23719356D+05 0.10178553D+06 v = 5.5, Vv(x)=0.23719356D+05, Vv'(x)=0.10178553D+06 MPBWA Test PBWA a W(a,x) W'(a,x) W(a,-x) W'(a,-x) --------------------------------------------------------------------- 0.5 0.18711529D+00 0.19157437D+00 -0.85565845D+00 0.44682493D+01 1.5 -0.21585269D-01 0.89987015D-01 -0.88586002D+01 -0.93971967D+01 0.0 0.30095491D+00 -0.71482331D+00 0.65996337D+00 0.17552224D+01 -0.5 -0.19340880D+00 -0.13474400D+01 0.64481479D+00 -0.67810115D+00 -1.5 -0.52665390D+00 0.82195159D+00 -0.28227741D+00 -0.14582283D+01 -5.0 0.89361847D-01 -0.18118641D+01 0.53860840D+00 0.26985526D+00 MPSI Test PSI x Psi(x) ------------------------ 0.25 -4.227453533 0.50 -1.963510026 0.75 -1.085860880 1.00 -0.577215665 1.25 -0.227453533 1.50 0.036489974 1.75 0.247472454 2.00 0.422784335 MRCTJ Test RCTJ n xjn(x) [xjn(x)]' -------------------------------------------- 0 -0.5440211109D+00 -0.8390715291D+00 1 0.7846694180D+00 -0.6224880527D+00 2 0.7794219363D+00 0.6287850307D+00 3 -0.3949584498D+00 0.8979094712D+00 4 -0.1055892851D+01 0.2739869063D-01 5 -0.5553451162D+00 -0.7782202931D+00 MRCTY Test RCTY n xyn(x) [xyn(x)]' -------------------------------------------- 0 0.8390715291D+00 -0.5440211109D+00 1 0.6279282638D+00 0.7762787027D+00 2 -0.6506930499D+00 0.7580668738D+00 3 -0.9532747888D+00 -0.3647106133D+00 4 -0.1659930220D-01 -0.9466350679D+00 5 0.9383354168D+00 -0.4857670106D+00 MRSWFO Test RSWFO x Rmn(1)(-ic,ix) Rmn'(1)(-ic,ix) Rmn(2)(-ic,ix) Rmn'(2)(-ic,ix) ------------------------------------------------------------------------ m= 2, n= 3, c= 5.0, cv = 2.1098058160, x= 0.00 0.0 0.00000000D+00 0.49911346D+00 -0.40071049D+00 0.33065682D+00 Wronskian check: Computed value = 0.20000000D+00 Exact value = 0.20000000D+00 m= 2, n= 3, c= 5.0, cv = 2.1098058160, x= 0.50 0.5 0.20215966D+00 0.19559661D+00 -0.15154835D+00 0.64482526D+00 Wronskian check: Computed value = 0.16000000D+00 Exact value = 0.16000000D+00 m= 2, n= 3, c= 5.0, cv = 2.1098058160, x= 1.00 1.0 0.10526737D+00 -0.54010624D+00 0.13065731D+00 0.27958491D+00 Wronskian check: Computed value = 0.10000000D+00 Exact value = 0.10000000D+00 m= 2, n= 3, c= 5.0, cv = 2.1098058160, x= 1.50 1.5 -0.11611246D+00 -0.89414690D-01 0.37405936D-01 -0.50118500D+00 Wronskian check: Computed value = 0.61538462D-01 Exact value = 0.61538462D-01 m= 2, n= 3, c= 5.0, cv = 2.1098058160, x= 5.00 5.0 0.36463251D-01 -0.83283065D-01 0.15549615D-01 0.17544481D+00 Wronskian check: Computed value = 0.76923077D-02 Exact value = 0.76923077D-02 MRSWFP Test RSWFP x Rmn(1)(c,x) Rmn'(1)(c,x) Rmn(2)(c,x) Rmn'(2)(c,x) -------------------------------------------------------------------------- m= 2, n= 3, c= 5.0, cv = 0.191359819110D+02, x= 1.00 1.00 0.16240735D-07 0.16240735D+01 -0.30786785D+07 0.30786784D+15 Wronskian check: Computed value = 0.10000000D+08 Exact value = 0.10000000D+08 Caution: This check is not accurate if it involves the subtraction of two similar numbers m= 2, n= 3, c= 5.0, cv = 0.191359819110D+02, x= 1.00 1.00 0.80600009D-02 0.15998506D+01 -0.62737713D+01 0.12299041D+04 Wronskian check: Computed value = 0.19950125D+02 Exact value = 0.19950125D+02 Caution: This check is not accurate if it involves the subtraction of two similar numbers m= 2, n= 3, c= 5.0, cv = 0.191359819110D+02, x= 1.10 1.10 0.13578875D+00 0.10702727D+01 -0.43693218D+00 0.35698419D+01 Wronskian check: Computed value = 0.95238095D+00 Exact value = 0.95238095D+00 Caution: This check is not accurate if it involves the subtraction of two similar numbers m= 2, n= 3, c= 5.0, cv = 0.191359819110D+02, x= 1.50 1.50 0.12002958D+00 -0.80657929D+00 0.12623910D+00 0.48469847D+00 Wronskian check: Computed value = 0.16000000D+00 Exact value = 0.16000000D+00 Caution: This check is not accurate if it involves the subtraction of two similar numbers m= 2, n= 3, c= 5.0, cv = 0.191359819110D+02, x= 5.00 5.00 0.39455888D-01 0.42556949D-01 -0.10099734D-01 0.20031280D+00 Wronskian check: Computed value = 0.83333333D-02 Exact value = 0.83333333D-02 Caution: This check is not accurate if it involves the subtraction of two similar numbers MSCKA Test SCKA KD= 1, m= 2, n= 2, c= 3.0, cv = 7.1511005241 Coefficients of Prolate function k C2k(c) ---------------------------- 0 0.1626690496D+01 1 0.1063977515D+01 2 0.2689538533D+00 3 0.3695888074D-01 4 0.3216541549D-02 5 0.1938336120D-03 6 0.8580981235D-05 7 0.2911465192D-06 8 0.7816633621D-08 9 0.1702580687D-09 10 0.3069742302D-11 11 0.4657802734D-13 12 0.6030562206D-15 13 0.6741296305D-17 14 0.6572610837D-19 15 0.5638578521D-21 16 0.4289438326D-23 17 0.2913442719D-25 18 0.1777629920D-27 19 0.9796837975D-30 20 0.4901043627D-32 21 0.2235618546D-34 22 0.9336596121D-37 23 0.3583318460D-39 24 0.1268177262D-41 25 0.4151902348D-44 26 0.1261125123D-46 27 0.3563600149D-49 KD= -1, m= 2, n= 2, c= 3.0, cv = 4.5264604622 Coefficients of Oblate function k C2k(-ic) ---------------------------- 0 0.5905230671D+01 1 -0.3703790431D+01 2 0.9115763203D+00 3 -0.1229718246D+00 4 0.1055821909D-01 5 -0.6296975358D-03 6 0.2764966163D-04 7 -0.9319481548D-06 8 0.2488442640D-07 9 -0.5395398302D-09 10 0.9689944027D-11 11 -0.1465339837D-12 12 0.1891655018D-14 13 -0.2109157336D-16 14 0.2051695632D-18 15 -0.1756553342D-20 16 0.1333827156D-22 17 -0.9044622775D-25 18 0.5510319571D-27 19 -0.3032707620D-29 20 0.1515279374D-31 21 -0.6904075732D-34 22 0.2880309029D-36 23 -0.1104366298D-38 24 0.3904952053D-41 25 -0.1277375016D-43 26 0.3876946082D-46 27 -0.1094720175D-48 MSCKB Test SCKB KD= 1, m= 2, n= 2, c= 3.0, cv = 7.1511005241 Coefficients of Prolate function k C2k(c) ---------------------------- 0 0.1626690496D+01 1 0.1063977515D+01 2 0.2689538533D+00 3 0.3695888074D-01 4 0.3216541549D-02 5 0.1938336120D-03 6 0.8580981235D-05 7 0.2911465192D-06 8 0.7816633621D-08 9 0.1702580687D-09 10 0.3069742302D-11 11 0.4657802734D-13 12 0.6030562206D-15 13 0.6741296305D-17 14 0.6572610837D-19 15 0.5638578521D-21 16 0.4289438326D-23 17 0.2913442719D-25 18 0.1777629920D-27 19 0.9796837975D-30 20 0.4901043627D-32 21 0.2235618546D-34 22 0.9336596121D-37 23 0.3583318463D-39 24 0.1268177129D-41 25 0.4151945114D-44 26 0.1260150123D-46 27 0.3703456542D-49 KD= -1, m= 2, n= 2, c= 3.0, cv = 4.5264604622 Coefficients of Oblate function k C2k(-ic) ---------------------------- 0 0.5905230671D+01 1 -0.3703790431D+01 2 0.9115763203D+00 3 -0.1229718246D+00 4 0.1055821909D-01 5 -0.6296975358D-03 6 0.2764966163D-04 7 -0.9319481548D-06 8 0.2488442640D-07 9 -0.5395398302D-09 10 0.9689944027D-11 11 -0.1465339837D-12 12 0.1891655018D-14 13 -0.2109157336D-16 14 0.2051695632D-18 15 -0.1756553342D-20 16 0.1333827156D-22 17 -0.9044622775D-25 18 0.5510319571D-27 19 -0.3032707620D-29 20 0.1515279374D-31 21 -0.6904075732D-34 22 0.2880309029D-36 23 -0.1104366297D-38 24 0.3904951670D-41 25 -0.1277362612D-43 26 0.3874100118D-46 27 -0.1053396507D-48 MSEGV Test SEGV m n c Lambda mn(c) --------------------------------------- 1 1 5.0 5.35042230 1 2 5.0 14.64295624 1 3 5.0 23.39761312 1 4 5.0 32.42194359 1 5 5.0 42.65818215 m n c Lambda mn(-ic) --------------------------------------- 1 1 5.0 -7.49338828 1 2 5.0 -7.12783752 1 3 5.0 2.75036721 1 4 5.0 8.69495925 1 5 5.0 18.43931577 MSDMN Test SDMN KD= 1, m= 2, n= 2, c= 3.0, cv = 7.1511005241 Coefficients of Prolate function r dr(c) ---------------------------- 0 0.9237882817D+00 2 -0.2901607696D-01 4 0.8142246173D-03 6 -0.1632270292D-04 8 0.2376699010D-06 10 -0.2601391701D-08 12 0.2209142844D-10 14 -0.1494812074D-12 16 0.8239302207D-15 18 -0.3768260778D-17 20 0.1452384658D-19 22 -0.4780280430D-22 24 0.1358919092D-24 26 -0.3369684134D-27 28 0.7351808877D-30 30 -0.1422072308D-32 32 0.2455364218D-35 34 -0.3807238841D-38 36 0.5330558187D-41 38 -0.6772436500D-44 40 0.7842816329D-47 42 -0.8312441497D-50 44 0.8093568132D-53 46 -0.7264412596D-56 48 0.6029595628D-59 50 -0.4641711770D-62 52 0.3323177752D-65 54 -0.2218273666D-68 KD= -1, m= 2, n= 2, c= 3.0, cv = 4.5264604622 Coefficients of Oblate function r dr(c) ---------------------------- 0 0.1115434000D+01 2 0.4888489020D-01 4 0.1600845667D-02 6 0.3509183384D-04 8 0.5416293446D-06 10 0.6176624069D-08 12 0.5407431236D-10 14 0.3745889118D-12 16 0.2103624480D-14 18 0.9768323113D-17 20 0.3812753620D-19 22 0.1268321726D-21 24 0.3638454446D-24 26 0.9093366844D-27 28 0.1997600767D-29 30 0.3887402422D-32 32 0.6748100420D-35 34 0.1051369240D-37 36 0.1478382470D-40 38 0.1885592788D-43 40 0.2191334024D-46 42 0.2330042829D-49 44 0.2275392454D-52 46 0.2047831733D-55 48 0.1703993699D-58 50 0.1314809415D-61 52 0.9433451703D-65 54 0.6309569734D-68 MSPHI Test SPHI n in(x) in'(x) -------------------------------------------- 0 0.1101323287D+04 0.9911909633D+03 1 0.9911909633D+03 0.9030850948D+03 2 0.8039659985D+03 0.7500011637D+03 3 0.5892079640D+03 0.5682828129D+03 4 0.3915204237D+03 0.3934477522D+03 5 0.2368395827D+03 0.2494166741D+03 MSPHJ SPHJ evaluates spherical Bessel J functions n x jn(x) jn'(x) 0 0.9050000000D+00 0.8689780718D+00 -0.2776712617D+00 1 0.9050000000D+00 0.2776712617D+00 0.2553399244D+00 2 0.9050000000D+00 0.5147914933D-01 0.1070221479D+00 3 0.9050000000D+00 0.6743927972D-02 0.2167173288D-01 4 0.9050000000D+00 0.6838294584D-03 0.2965864666D-02 5 0.9050000000D+00 0.5658597917D-04 0.3086737954D-03 n x jn(x) jn'(x) 0 0.1000000000D+02 -0.5440211109D-01 -0.7846694180D-01 1 0.1000000000D+02 0.7846694180D-01 -0.7009549945D-01 2 0.1000000000D+02 0.7794219363D-01 0.5508428371D-01 3 0.1000000000D+02 -0.3949584498D-01 0.9374053162D-01 4 0.1000000000D+02 -0.1055892851D+00 0.1329879757D-01 5 0.1000000000D+02 -0.5553451162D-01 -0.7226857814D-01 MSPHK Test SPHK n kn(x) kn'(x) -------------------------------------------- 0 0.7131404291D-05 -0.7844544720D-05 1 0.7844544720D-05 -0.8700313235D-05 2 0.9484767707D-05 -0.1068997503D-04 3 0.1258692857D-04 -0.1451953914D-04 4 0.1829561771D-04 -0.2173473743D-04 5 0.2905298451D-04 -0.3572740841D-04 MSPHY Test SPHY n yn(x) yn'(x) -------------------------------------------- 0 0.8390715291D-01 -0.6279282638D-01 1 0.6279282638D-01 0.7134858763D-01 2 -0.6506930499D-01 0.8231361788D-01 3 -0.9532747888D-01 -0.2693831344D-01 4 -0.1659930220D-02 -0.9449751377D-01 5 0.9383354168D-01 -0.5796005523D-01 MSTVH0 Test STVH0 x H0(x) ---------------------- 0.0 0.00000000E+00 5.0 -0.18521682E+00 10.0 0.11874368E+00 15.0 0.24772383E+00 20.0 0.94393698E-01 25.0 -0.10182482E+00 MSTVH1 Test STVH1 x H1(x) ----------------------- 0.0 -0.00000000E+00 5.0 0.80781195E+00 10.0 0.89183249E+00 15.0 0.66048730E+00 20.0 0.47268818E+00 25.0 0.53880362E+00 MSTVHV Test STVHV v Hv(x) ----------------------- 4.5 0.42012361D-05 4.5 0.17225555D-02 4.5 0.25963806D-01 4.5 0.14146911D+00 4.5 0.45717447D+00 4.5 0.10652365D+01 MSTVL0 Test STVL0 x L0(x) ----------------------- 0.0 0.00000000D+00 5.0 0.27105917D+02 10.0 0.28156522D+04 15.0 0.33964933D+06 20.0 0.43558283D+08 25.0 0.57745606D+10 30.0 0.78167230D+12 35.0 0.10733882D+15 40.0 0.14894775D+17 45.0 0.20834141D+19 50.0 0.29325538D+21 MSTVL1 Test STVL1 x L1(x) ----------------------- 0.0 0.00000000D+00 5.0 0.23728216D+02 10.0 0.26703583D+04 15.0 0.32812429D+06 20.0 0.42454973D+08 25.0 0.56578651D+10 30.0 0.76853204D+12 35.0 0.10579413D+15 40.0 0.14707396D+17 45.0 0.20601335D+19 50.0 0.29030786D+21 MSTVLV Test STVLV v x Lv(x) --------------------------------- 0.5 10.0 0.27785323D+04 1.5 10.0 0.24996698D+04 2.5 10.0 0.20254774D+04 3.5 10.0 0.14816746D+04 4.5 10.0 0.98173460D+03 5.5 10.0 0.59154277D+03 special_functions_test():: Normal end of execution. 3 December 2022 11:33:43.502 PM