function r9chm (a, c, x)
        real a, c, x, aa(4), bb(4), ct1, ct2, eps,
       1  g1, g2, g3, x2, xn0, xn1, xn2, xn3
        external r1mach
  c
        data eps /0.0/
  c
        if (eps.eq.0.0) eps = 4.0*r1mach(4)
  c
   10   aa(1) = 1.0
        bb(1) = 1.0
  c
        x2 = -0.5*x
        bb(2) = 1.0 + (1.0+a)*x2/c
        aa(2) = bb(2) + a*x/c
  c
        ct2 = x2/(1.0+c)
        bb(3) = 1.0 + (2.0+bb(2))*(2.0+a)*ct2/3.0
        aa(3) = bb(3) + (1.0+ct2)*a*x/c
  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 = 1.0 + ct2*(xn2-a)
          ct2 = ct2*(a+xn1)/(c+xn2)
          g2 = ct2*(c-xn1+(a+xn0)*x2/(ct1+2.0))
          g3 = ct2*x2*x2*(a+xn2)*(a-xn2)/(ct1*(ct1-2.0)*(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)
  c
          r9chm = aa(4)/bb(4)
          if (abs(r9chm-aa(1)/bb(1)).lt.eps*abs(r9chm)) 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 (40hr9chm   no convergence in 300 iterations, 40,
       1    1, 2)
  c
   40   return
        end