psi

Purpose

Computes the Psi (or Digamma) function.

Format

f = psi(z)
Parameters:z (NxK matrix) – data. z may be complex
Returns:f (NxK matrix) – the Psi function computed at z.

Examples

psi(1)

The solution printed is

-0.577215

Remarks

This program uses the analytical derivative of the log of the Lanczos series approximation for the Gamma function.

References

    1. Lanczos, SIAM JNA 1, 1964. pp. 86-96.
    1. Luke, ‘’The Special … approximations,’’ 1969 pp. 29-31.
    1. Luke, ‘’Algorithms … functions,’’ 1977.
    1. Spouge, SIAM JNA 31, 1994. pp. 931.
    1. Press, ‘’Numerical Recipes.’’
    1. Chang, ‘’Computation of special functions,’’ 1996.
  7. Original code by Paul Godfrey