!
!  *******  Fourier series of saw-tooth function for PLCM  *******
!
   subroutine fourexp( si_ex, z, t,  D, hpl, ndeg )

      implicit none

      real(8):: si_ex
      real(8):: z,   t
      real(8):: D,   hpl
      real(8):: s1,  sall
      real(8):: pi
      integer:: ndeg
      integer:: i,   n
      real(8),allocatable:: f(:)

!  ****  allocate  ****

      allocate ( f( ndeg ) )

!  ****  pi  ****

      pi = 4.0d0 * atan( 1.0d0 )

!  ****  calculate sin( n*pi*z/H )*exp( -(n*pi/H)**2*D*t )  ****


      do i = 1,ndeg
        f(i) = 2.0d0 / ( dfloat(i) * pi )                           &
        &      * sin( dfloat(i) * pi *z / hpl )                     &
        &      * exp( - ( dfloat( i ) * pi / hpl )**2 * D * t )        
      end do

!  ****  summation  ****

      s1 = 0.0d0
      do i = 1,ndeg
        s1 = s1 + f(i)
      end do

      si_ex = s1

      return 

    end subroutine fourexp