Gamma

Gamma[z] is the Euler gamma function .

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

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

Mathematical function (see Section A.3.10).

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 .

FullSimplify and FunctionExpand include transformation rules for Gamma.

See The Mathematica Book: Section 3.2.10.

Implementation Notes: see section A.9.4.

See also: Factorial, LogGamma, GammaRegularized, InverseGammaRegularized, PolyGamma, RiemannSiegelTheta.

Further Examples