double precision function d9chm (a, c, x) double precision a, c, x, aa(4), bb(4), ct1, ct2, eps, 1 g1, g2, g3, x2, xn0, xn1, xn2, xn3, d1mach external d1mach double precision bmax c data eps /0.0d0/ c if (eps.eq.0.0d0) eps = 4.0d0*d1mach(4) c 10 aa(1) = 1.0d0 bb(1) = 1.0d0 c x2 = -0.5d0*x bb(2) = 1.0d0 + (1.0d0+a)*x2/c aa(2) = bb(2) + a*x/c c ct2 = x2/(1.0d0+c) bb(3) = 1.0d0 + (2.0d0+bb(2))*(2.0d0+a)*ct2/3.0d0 aa(3) = bb(3) + (1.0d0+ct2)*a*x/c bmax = dmax1 (bb(1), bb(2), bb(3)) c do 30 i=3,300 xn0 = i xn1 = i - 1 xn2 = i - 2 xn3 = i - 3 ct1 = 2*i - 3 c ct2 = x2/(ct1*(c+xn1)) g1 = 1.0d0 + ct2*(xn2-a) ct2 = ct2*(a+xn1)/(c+xn2) g2 = ct2*(c-xn1+(a+xn0)*x2/(ct1+2.0d0)) g3 = ct2*x2*x2*(a+xn2)*(a-xn2)/(ct1*(ct1-2.0d0)*(c+xn3)) c bb(4) = g1*bb(3) + g2*bb(2) + g3*bb(1) aa(4) = g1*aa(3) + g2*aa(2) + g3*aa(1) bmax = dmax1 (bb(4), bmax) c d9chm = aa(4)/bb(4) if (dabs(d9chm-aa(1)/bb(1)).lt.eps*dabs(d9chm)) go to 40 c do 20 j=1,3 aa(j) = aa(j+1) bb(j) = bb(j+1) 20 continue 30 continue call seteru (40hd9chm no convergence in 300 iterations, 40, 1 1, 2) c 40 continue errest = d1mach(4)*dmax1(dabs(d9chm), 1.0d0) print 500, i, aa(4), bb(4), d9chm, bmax, errest 500 format (1x, i3, 3d15.5, 2e15.5) c return end