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.