samer@4: function [f] = zeta(z)
samer@4: % zeta - Riemann Zeta function
samer@4: %
samer@4: % zeta :: complex -> complex.
samer@4: %
samer@4: %tested on version 5.3.1
samer@4: %
samer@4: %      This program calculates the Riemann Zeta function
samer@4: %      for the elements of Z using the Dirichlet deta function.
samer@4: %      Z may be complex and any size. Best accuracy for abs(z)<80.
samer@4: %
samer@4: %      Has a pole at z=1, zeros for z=(-even integers),
samer@4: %      infinite number of zeros for z=1/2+i*y
samer@4: %
samer@4: %
samer@4: %see also: Eta, Deta, Lambda, Betad, Bern, Euler
samer@4: %see also: mhelp zeta
samer@4: 
samer@4: %Paul Godfrey
samer@4: %pgodfrey@conexant.com
samer@4: %3-24-01
samer@4: 
samer@4: zz=2.^z;
samer@4: k = zz./(zz-2);
samer@4: 
samer@4: f=k.*deta(z,1);
samer@4: 
samer@4: p=find(z==1);
samer@4: if ~isempty(p)
samer@4:    f(p)=Inf;
samer@4: end
samer@4: 
samer@4: return
samer@4: