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 .

Details

  • 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.

Examples

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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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Scope  (5)

Generalizations & Extensions  (11)

Applications  (5)

Properties & Relations  (9)

Possible Issues  (2)

Neat Examples  (2)

See Also

Factorial  LogGamma  GammaRegularized  InverseGammaRegularized  PolyGamma  RiemannSiegelTheta  GammaDistribution  QGamma  FactorialPower

Tutorials

Introduced in 1988
(1.0)