No BSD License
-
bern(n)
Bern Bernoulli number
-
betad(z)
BETAD Dirichlet Beta function
-
binomial(n,d)
BINOMIAL calculate the binomial coefficient
-
deta(z,k)
DETA Calculates Dirichlet functions of the form
-
erfz(zz)
ERFZ Error function for complex inputs
-
eta(z)
ETA Dirichlet Eta function
-
euler(n)
Euler Euler number
-
eulergamma
Euler-Mascheroni constant = -Psi(1) = 0.5772156649015328606...
-
fact(n)
FACT Vectorized Factorial function
-
factd(n)
FACTD Double Factorial function = n!!
-
gamma(z)
GAMMA Gamma function valid in the entire complex plane.
-
gammaln(z)
GAMMALOG Natural Log of the Gamma function valid in the entire complex plane.
-
genocchi(z)
Genocchi number
-
harm(z)
Harm Harmonic sum function valid in the entire (complex) plane.
-
lambda(z)
LAMBDA Dirichlet Lambda function
-
poch(z,n)
-
psi(z)
Psi Psi (or Digamma) function valid in the entire complex plane.
-
psin(n,z)
Psin Arbitrary order Polygamma function valid in the entire complex plane.
-
totient(n)
TOTIENT calculates the totient function (also
-
zeta(z)
ZETA Riemann Zeta function
-
View all files
from
Special Functions math library
by Paul Godfrey
Collection of Special Functions programs.
|
| zeta(z) |
function [f] = zeta(z)
%ZETA Riemann Zeta function
%
%usage: f = zeta(z)
%
%tested on version 5.3.1
%
% This program calculates the Riemann Zeta function
% for the elements of Z using the Dirichlet deta function.
% Z may be complex and any size. Best accuracy for abs(z)<80.
%
% Has a pole at z=1, zeros for z=(-even integers),
% infinite number of zeros for z=1/2+i*y
%
%
%see also: Eta, Deta, Lambda, Betad, Bern, Euler
%see also: mhelp zeta
%Paul Godfrey
%pgodfrey@conexant.com
%3-24-01
zz=2.^z;
k = zz./(zz-2);
f=k.*deta(z,1);
p=find(z==1);
if ~isempty(p)
f(p)=Inf;
end
return
%a demo of this function is
ezplot zeta
grid on
figure(2)
ezmesh('abs(zeta(x+i*y))',[0 1 .5 30])
view(75, 4)
|
|
Contact us at files@mathworks.com
