# Documentation

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# gamma

Gamma function

Y = gamma(X)

## Description

Y = gamma(X) returns the gamma function at the elements of X. X must be real.

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### Gamma Function

The gamma function is defined by the integral:

$\Gamma \left(x\right)={\int }_{0}^{\infty }{e}^{-t}{t}^{x-1}dt$

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

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

### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.

### Algorithms

The computation of gamma is based on algorithms outlined in [1]. Several different minimax rational approximations are used depending upon the value of A.

## References

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