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Highlights from
Special Functions math library

  • 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.

betad(z) 
function [f] = betad(z)
%BETAD Dirichlet Beta function
%
%usage: 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
%
%
%see also: Zeta, Deta, Eta, Lambda, Bern, Euler

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

f=deta(z,2);

return

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