Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / specfun-1.1.0 / zeta.m

diff --git a/octave_packages/specfun-1.1.0/zeta.m b/octave_packages/specfun-1.1.0/zeta.m
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+## 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