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Hypergeometric1F1RegularizedGammaRegularized

Gamma

FilledSmallSquareGamma[z] is the Euler gamma function .

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

FilledSmallSquareGamma[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.

FilledSmallSquareGamma[z] has no branch cut discontinuities.

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

FilledSmallSquareFullSimplify and FunctionExpand include transformation rules for Gamma.

FilledSmallSquare See The Mathematica Book: Section 3.2.10.

FilledSmallSquare Implementation Notes: see section A.9.4.

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

Further Examples

Hypergeometric1F1RegularizedGammaRegularized