### Highlights fromSpecial 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
• 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.

```function [f] = betad(z)
%
%
%tested on version 5.3.1
%
%      This program calculates the Dirichlet Beta function
%      for the elements of Z using the Dirichlet deta function.
%      Z may be complex and any size.
%
%      Note: this is NOT the beta function defined by
%            Gamma(x)*Gamma(y)/Gamma(x+y)
%
%      Has zeros for z=(-odd integers),
%      and infinite number of zeros for z=1/2+i*y
%
%