      double precision function dbesj1 (x)
c sept 1983 edition.  w. fullerton, c3, los alamos scientific lab.
c apr 1991  bug fix by boisvert@cam.nist.gov
      double precision x, bj1cs(19), ampl, theta, xsml, xmin, y,
     1  d1mach, dcsevl, dcos, dsqrt
      external d1mach, dcos, dcsevl, dsqrt, initds
c
c series for bj1        on the interval  0.          to  1.60000e+01
c                                        with weighted error   1.16e-33
c                                         log weighted error  32.93
c                               significant figures required  32.36
c                                    decimal places required  33.57
c
      data bj1 cs(  1) / -.1172614151 3332786560 6240574524 003 d+0    /
      data bj1 cs(  2) / -.2536152183 0790639562 3030884554 698 d+0    /
      data bj1 cs(  3) / +.5012708098 4469568505 3656363203 743 d-1    /
      data bj1 cs(  4) / -.4631514809 6250819184 2619728789 772 d-2    /
      data bj1 cs(  5) / +.2479962294 1591402453 9124064592 364 d-3    /
      data bj1 cs(  6) / -.8678948686 2788258452 1246435176 416 d-5    /
      data bj1 cs(  7) / +.2142939171 4379369150 2766250991 292 d-6    /
      data bj1 cs(  8) / -.3936093079 1831797922 9322764073 061 d-8    /
      data bj1 cs(  9) / +.5591182317 9468800401 8248059864 032 d-10   /
      data bj1 cs( 10) / -.6327616404 6613930247 7695274014 880 d-12   /
      data bj1 cs( 11) / +.5840991610 8572470032 6945563268 266 d-14   /
      data bj1 cs( 12) / -.4482533818 7012581903 9135059199 999 d-16   /
      data bj1 cs( 13) / +.2905384492 6250246630 6018688000 000 d-18   /
      data bj1 cs( 14) / -.1611732197 8414416541 2118186666 666 d-20   /
      data bj1 cs( 15) / +.7739478819 3927463729 8346666666 666 d-23   /
      data bj1 cs( 16) / -.3248693782 1119984114 3466666666 666 d-25   /
      data bj1 cs( 17) / +.1202237677 2274102272 0000000000 000 d-27   /
      data bj1 cs( 18) / -.3952012212 6513493333 3333333333 333 d-30   /
      data bj1 cs( 19) / +.1161678082 2664533333 3333333333 333 d-32   /
c
      data ntj1, xsml, xmin / 0, 2*0.d0 /
c
      if (ntj1.ne.0) go to 10
      ntj1 = initds (bj1cs, 19, 0.1*sngl(d1mach(3)))
c
      xsml = dsqrt (4.0d0*d1mach(3))
      xmin = 2.0d0*d1mach(1)
c
 10   y = dabs(x)
      if (y.gt.4.0d0) go to 20
c
      dbesj1 = 0.0d0
      if (y.eq.0.0d0) return
c
      if (y.le.xmin) call seteru (
     1  38hdbesj1  dabs(x) so small j1 underflows, 38, 1, 0)
      if (y.gt.xmin) dbesj1 = 0.5d0*x
      if (y.gt.xsml) dbesj1 = x*(.25d0 + dcsevl (.125d0*y*y-1.d0,
     1  bj1cs, ntj1) )
      return
c
 20   call d9b1mp (y, ampl, theta)
      dbesj1 = sign(ampl,x) * dcos(theta)
c
      return
      end