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Documentation / Mathematica / Built-in Functions / Mathematical Functions / Factorial Related /

Gamma

FilledSmallSquare Gamma[z] is the Euler gamma function .

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

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

FilledSmallSquare Mathematical function (see Section A.3.10).

FilledSmallSquare The gamma function satisfies .

FilledSmallSquare The incomplete gamma function satisfies .

FilledSmallSquare The generalized incomplete gamma function is given by the integral .

FilledSmallSquare Note that the arguments in the incomplete form of Gamma are arranged differently from those in the incomplete form of Beta.

FilledSmallSquare Gamma[z] has no branch cut discontinuities.

FilledSmallSquare Gamma[a, z] has a branch cut discontinuity in the complex z plane running from to .

FilledSmallSquare FullSimplify and FunctionExpand include transformation rules for Gamma.

FilledSmallSquare See Section 3.2.10.

FilledSmallSquare Implementation Notes: see Section A.9.4.

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

FilledSmallSquare New in Version 1.

Further Examples