This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

Gamma

Gamma[z]
is the Euler gamma function Gamma(z).
Gamma[a, z]
is the incomplete gamma function Gamma(a,z).
Gamma[a, z0, z1]
is the generalized incomplete gamma function Gamma(a,z_0)-Gamma(a,z_1).
  • 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 0.
  • For certain special arguments, Gamma automatically evaluates to exact values.
  • Gamma can be evaluated to arbitrary numerical precision.
  • Gamma automatically threads over lists.
New in 1