function besk1e (x)
c july 1980 version.  w. fullerton, c3, los alamos scientific lab.
      dimension bk1cs(11), ak1cs(17), ak12cs(14)
      external alog, besi1, csevl, exp, inits, r1mach, sqrt
c
c series for bk1        on the interval  0.          to  4.00000d+00
c                                        with weighted error   7.02e-18
c                                         log weighted error  17.15
c                               significant figures required  16.73
c                                    decimal places required  17.67
c
      data bk1 cs( 1) /    .0253002273 389477705e0 /
      data bk1 cs( 2) /   -.3531559607 76544876e0 /
      data bk1 cs( 3) /   -.1226111808 22657148e0 /
      data bk1 cs( 4) /   -.0069757238 596398643e0 /
      data bk1 cs( 5) /   -.0001730288 957513052e0 /
      data bk1 cs( 6) /   -.0000024334 061415659e0 /
      data bk1 cs( 7) /   -.0000000221 338763073e0 /
      data bk1 cs( 8) /   -.0000000001 411488392e0 /
      data bk1 cs( 9) /   -.0000000000 006666901e0 /
      data bk1 cs(10) /   -.0000000000 000024274e0 /
      data bk1 cs(11) /   -.0000000000 000000070e0 /
c
c series for ak1        on the interval  1.25000d-01 to  5.00000d-01
c                                        with weighted error   6.06e-17
c                                         log weighted error  16.22
c                               significant figures required  15.41
c                                    decimal places required  16.83
c
      data ak1 cs( 1) /    .2744313406 973883e0 /
      data ak1 cs( 2) /    .0757198995 3199368e0 /
      data ak1 cs( 3) /   -.0014410515 5647540e0 /
      data ak1 cs( 4) /    .0000665011 6955125e0 /
      data ak1 cs( 5) /   -.0000043699 8470952e0 /
      data ak1 cs( 6) /    .0000003540 2774997e0 /
      data ak1 cs( 7) /   -.0000000331 1163779e0 /
      data ak1 cs( 8) /    .0000000034 4597758e0 /
      data ak1 cs( 9) /   -.0000000003 8989323e0 /
      data ak1 cs(10) /    .0000000000 4720819e0 /
      data ak1 cs(11) /   -.0000000000 0604783e0 /
      data ak1 cs(12) /    .0000000000 0081284e0 /
      data ak1 cs(13) /   -.0000000000 0011386e0 /
      data ak1 cs(14) /    .0000000000 0001654e0 /
      data ak1 cs(15) /   -.0000000000 0000248e0 /
      data ak1 cs(16) /    .0000000000 0000038e0 /
      data ak1 cs(17) /   -.0000000000 0000006e0 /
c
c series for ak12       on the interval  0.          to  1.25000d-01
c                                        with weighted error   2.58e-17
c                                         log weighted error  16.59
c                               significant figures required  15.22
c                                    decimal places required  17.16
c
      data ak12cs( 1) /    .0637930834 3739001e0 /
      data ak12cs( 2) /    .0283288781 3049721e0 /
      data ak12cs( 3) /   -.0002475370 6739052e0 /
      data ak12cs( 4) /    .0000057719 7245160e0 /
      data ak12cs( 5) /   -.0000002068 9392195e0 /
      data ak12cs( 6) /    .0000000097 3998344e0 /
      data ak12cs( 7) /   -.0000000005 5853361e0 /
      data ak12cs( 8) /    .0000000000 3732996e0 /
      data ak12cs( 9) /   -.0000000000 0282505e0 /
      data ak12cs(10) /    .0000000000 0023720e0 /
      data ak12cs(11) /   -.0000000000 0002176e0 /
      data ak12cs(12) /    .0000000000 0000215e0 /
      data ak12cs(13) /   -.0000000000 0000022e0 /
      data ak12cs(14) /    .0000000000 0000002e0 /
c
      data ntk1, ntak1, ntak12, xmin, xsml / 3*0, 2*0. /
c
      if (ntk1.ne.0) go to 10
      ntk1 = inits (bk1cs, 11, 0.1*r1mach(3))
      ntak1 = inits (ak1cs, 17, 0.1*r1mach(3))
      ntak12 = inits (ak12cs, 14, 0.1*r1mach(3))
c
      xmin = exp (amax1(alog(r1mach(1)), -alog(r1mach(2))) + .01)
      xsml = sqrt (4.0*r1mach(3))
c
 10   if (x.le.0.) call seteru (29hbesk1e  x is zero or negative, 29,
     1  1, 2)
      if (x.gt.2.0) go to 20
c
      if (x.lt.xmin) call seteru (31hbesk1e  x so small k1 overflows,
     1  31, 2, 2)
      y = 0.
      if (x.gt.xsml) y = x*x
      besk1e = exp(x) * (alog(0.5*x)*besi1(x) +
     1  (0.75 + csevl (.5*y-1., bk1cs, ntk1))/x )
      return
c
 20   if (x.le.8.) besk1e = (1.25 + csevl ((16./x-5.)/3., ak1cs, ntak1))
     1  / sqrt(x)
      if (x.gt.8.) besk1e = (1.25 + csevl (16./x-1., ak12cs, ntak12))
     1  / sqrt(x)
c
      return
      end