1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
3 ## This program is free software; you can redistribute it and/or modify
4 ## it under the terms of the GNU General Public License as published by
5 ## the Free Software Foundation; either version 3 of the License, or
6 ## (at your option) any later version.
8 ## This program is distributed in the hope that it will be useful,
9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 ## GNU General Public License for more details.
13 ## You should have received a copy of the GNU General Public License
14 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
17 ## @deftypefn {Function File} {@var{z} =} zeta (@var{t})
18 ## Compute the Riemann's Zeta function.
27 for j = 1:prod(size(t))
29 if(imag(t(j)) == 0 && real(t(j)) > 1)
30 F= @(x) 1./(gamma(t(j))).*x.^(t(j)-1)./(exp(x)-1);
38 z(j) += (-1).^(k-1)./(k.^t(j));
40 z(j) = 1./(1-2.^(1-t(j))).*z(j);
43 z(j) = 2.^t(j).*pi.^(t(j)-1).*sin(pi.*t(j)./2).*gamma(1-t(j)).*zeta(1-t(j));