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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.

totient(n) 
function [t] = totient(n)
%TOTIENT  calculates the totient function (also
%         called the Euler Phi function) of any
%         positive integer n.
%
%Usage:   f = totient(n)
%
%         The totient function computes the number of
%         integers from the set (1...n-1) that are
%         relatively prime to n. It can be used to
%         describe the multiplicative structure of
%         all Galois fields GF(q).
%
%         n can be any size
%
%         Tested under version 5.2.0
%
%Ref: "Error Control Systems" by S.B Wicker
%
%see also Primes, Factor

% Paul Godfrey
% pgodfrey@conexant.com
% 10-23-2001

[r c]=size(n);
n=reshape(n,1,r*c);
t=zeros(1,r*c);
f=zeros(1,10);

for k=1:r*c;
    nk=n(k);
    f=unique(factor(nk));
    t(k)=nk*prod(1-1./f);
end
t=reshape(t,r,c);
p=find(n==1);
t(p)=1;
t=round(t);
return

%a demo of this program is
n=(1:50).';
t=totient(n);
[n t]

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