function besy0 (x) c august 1980 version. w. fullerton, c3, los alamos scientific lab. dimension by0cs(13), bm0cs(21), bth0cs(24) external besj0, csevl, inits, r1mach c c series for by0 on the interval 0. to 1.60000d+01 c with weighted error 1.20e-17 c log weighted error 16.92 c significant figures required 16.15 c decimal places required 17.48 c data by0 cs( 1) / -.0112778393 92865573e0 / data by0 cs( 2) / -.1283452375 6042035e0 / data by0 cs( 3) / -.1043788479 9794249e0 / data by0 cs( 4) / .0236627491 83969695e0 / data by0 cs( 5) / -.0020903916 47700486e0 / data by0 cs( 6) / .0001039754 53939057e0 / data by0 cs( 7) / -.0000033697 47162423e0 / data by0 cs( 8) / .0000000772 93842676e0 / data by0 cs( 9) / -.0000000013 24976772e0 / data by0 cs(10) / .0000000000 17648232e0 / data by0 cs(11) / -.0000000000 00188105e0 / data by0 cs(12) / .0000000000 00001641e0 / data by0 cs(13) / -.0000000000 00000011e0 / c c series for bm0 on the interval 0. to 6.25000d-02 c with weighted error 4.98e-17 c log weighted error 16.30 c significant figures required 14.97 c decimal places required 16.96 c data bm0 cs( 1) / .0928496163 7381644e0 / data bm0 cs( 2) / -.0014298770 7403484e0 / data bm0 cs( 3) / .0000283057 9271257e0 / data bm0 cs( 4) / -.0000014330 0611424e0 / data bm0 cs( 5) / .0000001202 8628046e0 / data bm0 cs( 6) / -.0000000139 7113013e0 / data bm0 cs( 7) / .0000000020 4076188e0 / data bm0 cs( 8) / -.0000000003 5399669e0 / data bm0 cs( 9) / .0000000000 7024759e0 / data bm0 cs(10) / -.0000000000 1554107e0 / data bm0 cs(11) / .0000000000 0376226e0 / data bm0 cs(12) / -.0000000000 0098282e0 / data bm0 cs(13) / .0000000000 0027408e0 / data bm0 cs(14) / -.0000000000 0008091e0 / data bm0 cs(15) / .0000000000 0002511e0 / data bm0 cs(16) / -.0000000000 0000814e0 / data bm0 cs(17) / .0000000000 0000275e0 / data bm0 cs(18) / -.0000000000 0000096e0 / data bm0 cs(19) / .0000000000 0000034e0 / data bm0 cs(20) / -.0000000000 0000012e0 / data bm0 cs(21) / .0000000000 0000004e0 / c c series for bth0 on the interval 0. to 6.25000d-02 c with weighted error 3.67e-17 c log weighted error 16.44 c significant figures required 15.53 c decimal places required 17.13 c data bth0cs( 1) / -.2463916377 4300119e0 / data bth0cs( 2) / .0017370983 07508963e0 / data bth0cs( 3) / -.0000621836 33402968e0 / data bth0cs( 4) / .0000043680 50165742e0 / data bth0cs( 5) / -.0000004560 93019869e0 / data bth0cs( 6) / .0000000621 97400101e0 / data bth0cs( 7) / -.0000000103 00442889e0 / data bth0cs( 8) / .0000000019 79526776e0 / data bth0cs( 9) / -.0000000004 28198396e0 / data bth0cs(10) / .0000000001 02035840e0 / data bth0cs(11) / -.0000000000 26363898e0 / data bth0cs(12) / .0000000000 07297935e0 / data bth0cs(13) / -.0000000000 02144188e0 / data bth0cs(14) / .0000000000 00663693e0 / data bth0cs(15) / -.0000000000 00215126e0 / data bth0cs(16) / .0000000000 00072659e0 / data bth0cs(17) / -.0000000000 00025465e0 / data bth0cs(18) / .0000000000 00009229e0 / data bth0cs(19) / -.0000000000 00003448e0 / data bth0cs(20) / .0000000000 00001325e0 / data bth0cs(21) / -.0000000000 00000522e0 / data bth0cs(22) / .0000000000 00000210e0 / data bth0cs(23) / -.0000000000 00000087e0 / data bth0cs(24) / .0000000000 00000036e0 / c c twodpi = 2.0/pi data twodpi / 0.6366197723 6758134e0 / data pi4 / 0.7853981633 9744831e0 / data alnhaf / -0.6931471805 59945309e0 / data nty0, ntm0, ntth0, xsml, xmax / 3*0, 2*0./ c if (nty0.ne.0) go to 10 nty0 = inits (by0cs, 13, 0.1*r1mach(3)) ntm0 = inits (bm0cs, 21, 0.1*r1mach(3)) ntth0 = inits (bth0cs, 24, 0.1*r1mach(3)) c xsml = sqrt (4.0*r1mach(3)) xmax = 1.0/r1mach(4) c 10 if (x.le.0.) call seteru (29hbesy0 x is zero or negative, 29, 1 1, 2) if (x.gt.4.0) go to 20 c y = 0. if (x.gt.xsml) y = x*x besy0 = twodpi*(alnhaf+alog(x))*besj0(x) + .375 + 1 csevl (.125*y-1., by0cs, nty0) return c 20 if (x.gt.xmax) call seteru ( 1 37hbesy0 no precision because x is big, 37, 2, 2) c z = 32.0/x**2 - 1.0 ampl = (0.75 + csevl (z, bm0cs, ntm0)) / sqrt(x) theta = x - pi4 + csevl (z, bth0cs, ntth0) / x besy0 = ampl * sin (theta) c return end