function [ p2, dp2, p1 ] = legendre_ss_recur ( x, n, c )
%*****************************************************************************80
%
%% legendre_ss_recur() finds the value and derivative of a Legendre polynomial.
%
% Discussion:
%
% The Stroud and Secrest reference did not print a specific computer program
% for the Gauss-Legendre case. Therefore, this code is based on the
% printed code for the Gauss-Jacobi case, with ALPHA and BETA set to 0.
% This means that the LEGENDRE_SS_ROOT and LEGENDRE_SS_RECUR routines,
% while appropriate for this computation, do not use the standard
% normalization for the Legendre polynomials in which Pn(1) = 1.
% The unusual scaling does not, however, affect the location of the
% roots, which is the primary thing of interest.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 12 October 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real X, the point at which polynomials are evaluated.
%
% integer N, the order of the polynomial to be computed.
%
% real C(N), the recursion coefficients.
%
% Output:
%
% real P2, the value of P(N)(X).
%
% real DP2, the value of P'(N)(X).
%
% real P1, the value of P(N-1)(X).
%
p1 = 1.0;
dp1 = 0.0;
p2 = x;
dp2 = 1.0;
for i = 2 : n
p0 = p1;
dp0 = dp1;
p1 = p2;
dp1 = dp2;
p2 = x * p1 - c(i) * p0;
dp2 = x * dp1 + p1 - c(i) * dp0;
end
return
end