      function besk0 (x)
c april 1977 version.  w. fullerton, c3, los alamos scientific lab.
      dimension bk0cs(11)
      external alog, besi0, besk0e, csevl, exp, inits, r1mach, sqrt
c
c series for bk0        on the interval  0.          to  4.00000d+00
c                                        with weighted error   3.57e-19
c                                         log weighted error  18.45
c                               significant figures required  17.99
c                                    decimal places required  18.97
c
      data bk0 cs( 1) /   -.0353273932 3390276872e0 /
      data bk0 cs( 2) /    .3442898999 246284869e0 /
      data bk0 cs( 3) /    .0359799365 1536150163e0 /
      data bk0 cs( 4) /    .0012646154 1144692592e0 /
      data bk0 cs( 5) /    .0000228621 2103119451e0 /
      data bk0 cs( 6) /    .0000002534 7910790261e0 /
      data bk0 cs( 7) /    .0000000019 0451637722e0 /
      data bk0 cs( 8) /    .0000000000 1034969525e0 /
      data bk0 cs( 9) /    .0000000000 0004259816e0 /
      data bk0 cs(10) /    .0000000000 0000013744e0 /
      data bk0 cs(11) /    .0000000000 0000000035e0 /
c
      data ntk0, xsml, xmax / 0, 0., 0. /
c
      if (ntk0.ne.0) go to 10
      ntk0 = inits (bk0cs, 11, 0.1*r1mach(3))
      xsml = sqrt (4.0*r1mach(3))
      xmax = -alog(r1mach(1))
      xmax = xmax - 0.5*xmax*alog(xmax)/(xmax+0.5) - 0.01
c
 10   if (x.le.0.) call seteru (29hbesk0   x is zero or negative, 29,
     1  2, 2)
      if (x.gt.2.) go to 20
c
      y = 0.
      if (x.gt.xsml) y = x*x
      besk0 = -alog(0.5*x)*besi0(x) - .25 + csevl (.5*y-1., bk0cs, ntk0)
      return
c
 20   besk0 = 0.
      if (x.gt.xmax) call seteru (30hbesk0   x so big k0 underflows, 30,
     1  1, 0)
      if (x.gt.xmax) return
c
      besk0 = exp(-x) * besk0e(x)
c
      return
      end