The Digamma or Psi Function

ASA103 is a FORTRAN90 library which evaluates the digamma or psi function, by Jose Bernardo.

ASA103 is Applied Statistics Algorithm 103.


ASA103 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ASA121, a FORTRAN90 library which evaluates the trigamma function.

FN, a FORTRAN90 library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta, confluent hypergeometric, cosine integral, Dawson's integral, digamma (psi), error, exponential integral, gamma, hyperbolic cosine integral, hyperbolic sine integral, incomplete gamma, log gamma, logarithmic integral, Pochhammer, psi, sine integral, Spence; by Wayne Fullerton.

SPECFUN, a FORTRAN90 library which computes special functions, including the Psi or Digamma function.

TEST_VALUES, a FORTRAN90 library which contains sample values for a number of distributions.

TOMS708, a FORTRAN90 library which includes routines to evaluate the digamma function.


Original FORTRAN77 version by Jose Bernardo; FORTRAN90 version by John Burkardt.


  1. Jose Bernardo,
    Algorithm AS 103: Psi ( Digamma ) Function,
    Applied Statistics,
    Volume 25, Number 3, 1976, pages 315-317.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 18 January 2008.