/usr/share/octave/packages/specfun-1.1.0/laguerre.m is in octave-specfun 1.1.0-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 | ## Copyright (C) 2008 Eric Chassande-Mottin
##
## 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{y} = } laguerre (@var{x},@var{n})
## @deftypefnx {Function File} {[@var{y} @var{p}]= } laguerre (@var{x},@var{n})
##
## Compute the value of the Laguerre polynomial of order @var{n} for each element of @var{x}
##
## @end deftypefn
function [y,p]=laguerre(x,n)
if (nargin != 2)
print_usage;
elseif (n < 0 || !isscalar (n))
error("second argument 'n' must be a positive integer");
endif
p0=1;
p1=[-1 1];
if (n==0)
p=p0;
elseif (n==1)
p=p1;
elseif (n > 1)
% recursive calculation of the polynomial coefficients
for k=2:n
p=zeros(1,k+1);
p(1) = -p1(1)/k;
p(2) = ((2*k-1)*p1(1)-p1(2))/k;
if (k > 2)
p(3:k) = ((2*k-1)*p1(2:k-1)-p1(3:k)-(k-1)*p0(1:k-2))/k;
endif
p(k+1) = ((2*k-1)*p1(k)-(k-1)*p0(k-1))/k;
p0=p1;
p1=p;
endfor
endif
y=polyval(p,x);
endfunction
%!test
%! x=rand;
%! y1=laguerre(x,0);
%! p0=[1];
%! y2=polyval(p0,x);
%! assert(y1-y2,0,eps);
%!test
%! x=rand;
%! y1=laguerre(x,1);
%! p1=[-1 1];
%! y2=polyval(p1,x);
%! assert(y1-y2,0,eps);
%!test
%! x=rand;
%! y1=laguerre(x,2);
%! p2=[.5 -2 1];
%! y2=polyval(p2,x);
%! assert(y1-y2,0,eps);
%!test
%! x=rand;
%! y1=laguerre(x,3);
%! p3=[-1/6 9/6 -18/6 1];
%! y2=polyval(p3,x);
%! assert(y1-y2,0,eps);
%!test
%! x=rand;
%! y1=laguerre(x,4);
%! p4=[1/24 -16/24 72/24 -96/24 1];
%! y2=polyval(p4,x);
%! assert(y1-y2,0,eps);
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