lqna Subroutine

subroutine lqna ( n, x, qn, qd )

  !*****************************************************************************80
  !
  !! LQNA computes Legendre function Qn(x) and derivatives Qn'(x).
  !
  !  Licensing:
  !
  !    This routine is copyrighted by Shanjie Zhang and Jianming Jin.  However, 
  !    they give permission to incorporate this routine into a user program 
  !    provided that the copyright is acknowledged.
  !
  !  Modified:
  !
  !    19 July 2012
  !
  !  Author:
  !
  !    Shanjie Zhang, Jianming Jin
  !
  !  Reference:
  !
  !    Shanjie Zhang, Jianming Jin,
  !    Computation of Special Functions,
  !    Wiley, 1996,
  !    ISBN: 0-471-11963-6,
  !    LC: QA351.C45.
  !
  !  Parameters:
  !
  !    Input, integer ( kind = 4 ) N, the degree of Qn(x).
  !
  !    Input, real ( kind = 8 ) X, the argument of Qn(x).
  !
  !    Output, real ( kind = 8 ) QN(0:N), QD(0:N), the values of
  !    Qn(x) and Qn'(x).
  !
  implicit none

  integer ( kind = 4 ) n

  integer ( kind = 4 ) k
  real ( kind = 8 ) q0
  real ( kind = 8 ) q1
  real ( kind = 8 ) qd(0:n)
  real ( kind = 8 ) qf
  real ( kind = 8 ) qn(0:n)
  real ( kind = 8 ) x

  if ( abs ( x ) == 1.0D+00 ) then

     do k = 0, n
        qn(k) = 1.0D+300
        qd(k) = -1.0D+300
     end do

  else if ( abs ( x ) < 1.0D+00 ) then

     q0 = 0.5D+00 * log ( ( 1.0D+00 + x ) / ( 1.0D+00 - x ) )
     q1 = x * q0 - 1.0D+00
     qn(0) = q0
     qn(1) = q1
     qd(0) = 1.0D+00 / ( 1.0D+00 - x * x )
     qd(1) = qn(0) + x * qd(0)
     do k = 2, n
        qf = ( ( 2 * k - 1 ) * x * q1 - ( k - 1 ) * q0 ) / k
        qn(k) = qf
        qd(k) = ( qn(k-1) - x * qf ) * k / ( 1.0D+00 - x * x )
        q0 = q1
        q1 = qf
     end do

  end if

  return
end subroutine lqna