# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Gamma

Gamma[z]
is the Euler gamma function .

Gamma[a,z]
is the incomplete gamma function .

Gamma[a,z0,z1]
is the generalized incomplete gamma function .

## DetailsDetails

• Mathematical function, suitable for both symbolic and numerical manipulation.
• The gamma function satisfies .
• The incomplete gamma function satisfies .
• The generalized incomplete gamma function is given by the integral .
• Note that the arguments in the incomplete form of Gamma are arranged differently from those in the incomplete form of Beta.
• Gamma[z] has no branch cut discontinuities.
• Gamma[a,z] has a branch cut discontinuity in the complex z plane running from to .
• For certain special arguments, Gamma automatically evaluates to exact values.
• Gamma can be evaluated to arbitrary numerical precision.
• Gamma automatically threads over lists.

## ExamplesExamplesopen allclose all

### Basic Examples  (4)Basic Examples  (4)

Integer values:

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Half-integer values:

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Evaluate numerically for complex arguments:

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