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## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@uta.edu>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{coefs}=} legendrepoly (@var{order},@var{x})
##
## Compute the coefficients of the Legendre polynomial, given the
## @var{order}. We calculate the Legendre polynomial using the recurrence
## relations, Pn+1(x) = inv(n+1)*((2n+1)*x*Pn(x) - nPn-1(x)).
##
## If the value @var{x} is specified, the polynomial is also evaluated,
## otherwise just the return the coefficients of the polynomial are returned.
##
## This is NOT the generalized Legendre polynomial.
##
## @end deftypefn
function h = legendrepoly (order, val)
if (nargin < 1 || nargin > 2)
print_usage
endif
h_prev = [0 1];
h_now = [1 0];
if order == 0
h=h_prev;
else
h=h_now;
endif
for ord=2:order
x=[];
y=[];
if (length(h_now) < (1+ord))
x=0;
endif
y=zeros(1,(1+ord)-length(h_prev));
p1=[h_now, x];
p3=[y, h_prev];
h=((2*ord -1).*p1 -(ord -1).*p3)./(ord);
h_prev=h_now;
h_now=h;
endfor
if nargin == 2
h=polyval(h,val);
endif
endfunction
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