# Gamma Function

A Gamma Function is a factorial function with its argument shifted down by 1.

**Example(s):**- a Digamma Function.
- a Trigamma Function.
- a Polygamma Function.
- …

**Counter-Example(s):****See:**Analytic Expression, Bessel Function, Weibull Distribution.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/gamma_function Retrieved:2014-12-7.
- In mathematics, the
**gamma function**(represented by the capital Greek letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if*n*is a positive integer: :[math]\displaystyle{ \Gamma(n) = (n-1)! }[/math]The gamma function is defined for all complex numbers except the negative integers and zero. For complex numbers with a positive real part, it is defined via a convergent improper integral: :[math]\displaystyle{ \Gamma(t) = \int_0^\infty x^{t-1} e^{-x}\,dx. }[/math] This integral function is extended by analytic continuation to all complex numbers except the non-positive integers (where the function has simple poles), yielding the meromorphic function we call the gamma function.

The gamma function is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics.

- In mathematics, the

### 2009

- http://en.wiktionary.org/wiki/gamma_function
- (analysis) A mathematical function which generalizes the notion of a factorial, taking any real value as input.