program test_hopf
      implicit none
      real*8 a(5), taur, ex, e, e1, x, expint
      integer i
      data a/0.71044609d0,-0.2830385d0,0.57975839d0,-0.75751038d0,
     *       0.45026781d0/
      
      taur = 1.d-7
      x = a(1)
      if (taur.gt.160.) goto 10
      ex = exp(-taur)
      e1 = expint(taur)
      e = e1
      do i=1,4
         e = (ex - taur*e)/i
         x = x + e*a(i+1)
      end do
   10 continue
      write(*,*) 'taur=', taur, ' Hopf=', x
      end