Highlights from Special Functions math library

• bern(n)Bern Bernoulli number
• 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
• eulergammaEuler-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

Special Functions math library

Paul Godfrey (view profile)

23 Oct 2001 (Updated )

Collection of Special Functions programs.

lambda(z)
```function [f] = lambda(z)
%LAMBDA  Dirichlet Lambda function
%
%usage: f = lambda(z)
%
%tested on version 5.3.1
%
%      This program calculates the Dirichlet Lambda function
%      for the elements of Z using the Dirichlet deta function.
%      Z may be complex and any size.
%
%      Has a pole at z=1, zeros for z=(-even integers),
%      z=0+i*k2Pi/ln(2), and an
%      infinite number of zeros for z=1/2+i*y
%
%

%Paul Godfrey
%pgodfrey@conexant.com
%3-24-01

zz=2.^z;
k = (zz-1)./(zz-2);

f=k.*deta(z,1);

p=find(z==1);
if ~isempty(p)
f(p)=Inf;
end

return
```