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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
  • 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

by

 

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
%
%
%see also: Zeta, Eta, Betad, Bern, Euler

%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

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