double precision function dbesk1 (x)
c july 1980 edition.  w. fullerton, c3, los alamos scientific lab.
      double precision x, bk1cs(16), xmax, xmin, xsml, y,
     1  d1mach, dcsevl, dbesi1, dbsk1e, dexp, dlog, dsqrt
      external d1mach, dbesi1, dbsk1e, dcsevl, dexp, dlog, dsqrt, initds
c
c series for bk1        on the interval  0.          to  4.00000e+00
c                                        with weighted error   9.16e-32
c                                         log weighted error  31.04
c                               significant figures required  30.61
c                                    decimal places required  31.64
c
      data bk1 cs(  1) / +.2530022733 8947770532 5311208685 33 d-1     /
      data bk1 cs(  2) / -.3531559607 7654487566 7238316918 01 d+0     /
      data bk1 cs(  3) / -.1226111808 2265714823 4790679300 42 d+0     /
      data bk1 cs(  4) / -.6975723859 6398643501 8129202960 83 d-2     /
      data bk1 cs(  5) / -.1730288957 5130520630 1765073689 79 d-3     /
      data bk1 cs(  6) / -.2433406141 5659682349 6007350301 64 d-5     /
      data bk1 cs(  7) / -.2213387630 7347258558 3152525451 26 d-7     /
      data bk1 cs(  8) / -.1411488392 6335277610 9583302126 08 d-9     /
      data bk1 cs(  9) / -.6666901694 1993290060 8537512643 73 d-12    /
      data bk1 cs( 10) / -.2427449850 5193659339 2631968648 53 d-14    /
      data bk1 cs( 11) / -.7023863479 3862875971 7837971200 00 d-17    /
      data bk1 cs( 12) / -.1654327515 5100994675 4910293333 33 d-19    /
      data bk1 cs( 13) / -.3233834745 9944491991 8933333333 33 d-22    /
      data bk1 cs( 14) / -.5331275052 9265274999 4666666666 66 d-25    /
      data bk1 cs( 15) / -.7513040716 2157226666 6666666666 66 d-28    /
      data bk1 cs( 16) / -.9155085717 6541866666 6666666666 66 d-31    /
c
      data ntk1, xmin, xsml, xmax / 0, 3*0.d0 /
c
      if (ntk1.ne.0) go to 10
      ntk1 = initds (bk1cs, 16, 0.1*sngl(d1mach(3)))
      xmin = dexp (dmax1(dlog(d1mach(1)), -dlog(d1mach(2))) + 0.01d0)
      xsml = dsqrt (4.0d0*d1mach(3))
      xmax = -dlog(d1mach(1))
      xmax = xmax - 0.5d0*xmax*dlog(xmax)/(xmax+0.5d0) - 0.01d0
c
 10   if (x.le.0.d0) call seteru (29hdbesk1  x is zero or negative,
     1  29, 2, 2)
      if (x.gt.2.0d0) go to 20
c
      if (x.lt.xmin) call seteru (31hdbesk1  x so small k1 overflows,
     1  31, 3, 2)
      y = 0.d0
      if (x.gt.xsml) y = x*x
      dbesk1 = dlog(0.5d0*x)*dbesi1(x) + (0.75d0 + dcsevl (.5d0*y-1.d0,
     1  bk1cs, ntk1))/x
      return
c
 20   dbesk1 = 0.d0
      if (x.gt.xmax) call seteru (30hdbesk1  x so big k1 underflows,
     1  30, 1, 0)
      if (x.gt.xmax) return
c
      dbesk1 = dexp(-x) * dbsk1e(x)
c
      return
      end