/usr/share/octave/packages/specfun-1.1.0/zeta.m is in octave-specfun 1.1.0-1build1.
This file is owned by root:root, with mode 0o644.
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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 | ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
##
## 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{z} =} zeta (@var{t})
## Compute the Riemann's Zeta function.
## @seealso{Si}
## @end deftypefn
function z = zeta(t)
if (nargin != 1)
print_usage;
endif
z = zeros(size(t));
for j = 1:prod(size(t))
if(real(t(j)) >= 0)
if(imag(t(j)) == 0 && real(t(j)) > 1)
F= @(x) 1./(gamma(t(j))).*x.^(t(j)-1)./(exp(x)-1);
z(j) = quad(F,0,Inf);
elseif(t(j) == 0)
z(j) = -0.5;
elseif(t(j) == 1)
z(j) = Inf;
else
for k = 1:100
z(j) += (-1).^(k-1)./(k.^t(j));
endfor
z(j) = 1./(1-2.^(1-t(j))).*z(j);
endif
else
z(j) = 2.^t(j).*pi.^(t(j)-1).*sin(pi.*t(j)./2).*gamma(1-t(j)).*zeta(1-t(j));
endif
endfor
endfunction
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