# Difference between revisions of "Manuals/calci/GAMMAFUNCTION"

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*Gamma function is defined for all complex numbers except the non-positive integers. | *Gamma function is defined for all complex numbers except the non-positive integers. | ||

*For complex numbers with a positive real part, it is defined via a convergent improper integral: | *For complex numbers with a positive real part, it is defined via a convergent improper integral: | ||

− | <math>\Gamma (z) = \int\limits_{0}^{infty} x^{z-1} e^{-x} dx </math> | + | <math>\Gamma (z) = \int\limits_{0}^{\infty} x^{z-1} e^{-x} dx </math> |

## Revision as of 15:05, 28 November 2016

**GAMMAFUNCTION (z)**

- is any positive real number.

## Description

- This function gives the value of the Gamma function.
- The Gamma function is defined to be an extension of the factorial to complex and real number arguments.
- That is, if n is a positive integer:

- Gamma function is defined for all complex numbers except the non-positive integers.
- For complex numbers with a positive real part, it is defined via a convergent improper integral: