# gamma, gammainc, gammaln

## Purpose

Gamma function.

## Synopsis

    y = gamma(a)
    y = gammainc(x,a)
    y = gammaln(a)

## Description

`y = gamma(a)` returns the gamma function evaluated at the elements of `a`. The gamma function is defined by the integral:

The gamma function interpolates the factorial function. For integer `n`

    gamma(n+1) = n! = prod(1:n)

`y = gammainc(x,a)` returns the incomplete gamma function defined by

`y = gammaln(a)` returns the logarithm of the gamma function,

    gammaln(a) = log(gamma(a))

`gammaln` avoids the underflow and overflow that may occur if it is computed directly using `log(gamma(a))`.

## Algorithm

The computations of `gamma` and `gammaln` are based on algorithms outlined in [1]. Several different minimax rational approximations are used depending upon the value of `a`. Computation of the incomplete gamma function is based on the algorithm in [2].

## References

[1] J. Cody, An Overview of Software Development for Special Functions, Lecture Notes in Mathematics, 506, Numerical Analysis Dundee, G. A. Watson (ed.), Springer Verlag, Berlin, 1976.

[2] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sec. 6.5.

(c) Copyright 1994 by The MathWorks, Inc.