1## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@uta.edu>
2##
3## This program is free software; you can redistribute it and/or modify it under
4## the terms of the GNU General Public License as published by the Free Software
5## Foundation; either version 3 of the License, or (at your option) any later
6## version.
7##
8## This program is distributed in the hope that it will be useful, but WITHOUT
9## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
11## details.
12##
13## You should have received a copy of the GNU General Public License along with
14## this program; if not, see <http://www.gnu.org/licenses/>.
15
16## -*- texinfo -*-
17## @deftypefn {Function File} {@var{coefs}=} legendrepoly (@var{order},@var{x})
18##
19## Compute the coefficients of the Legendre polynomial, given the
20## @var{order}. We calculate the Legendre polynomial using the recurrence
21## relations, Pn+1(x) = inv(n+1)*((2n+1)*x*Pn(x) - nPn-1(x)).
22##
23## If the value @var{x} is specified, the polynomial is also evaluated,
24## otherwise just the return the coefficients of the polynomial are returned.
25##
26## This is NOT the generalized Legendre polynomial.
27##
28## @end deftypefn
29
30function h = legendrepoly (order, val)
31  if (nargin < 1 || nargin > 2)
32    print_usage
33  endif
34
35  h_prev = [0 1];
36  h_now  = [1 0];
37
38  if order == 0
39    h=h_prev;
40  else
41    h=h_now;
42  endif
43
44  for ord=2:order
45    x=[];
46    y=[];
47    if (length(h_now) < (1+ord))
48      x=0;
49    endif
50    y=zeros(1,(1+ord)-length(h_prev));
51    p1=[h_now, x];
52    p3=[y, h_prev];
53    h=((2*ord -1).*p1  -(ord -1).*p3)./(ord);
54    h_prev=h_now;
55    h_now=h;
56  endfor
57
58  if nargin == 2
59    h=polyval(h,val);
60  endif
61
62endfunction
63