Gamma Functions and Related Functions

As the basis for many other special functions, the Wolfram Language supports efficient arbitrary-precision evaluation of gamma functions, as well as an extensive web of relations and transformationsmany original to Wolfram Research.

ReferenceReference

Gamma complete and incomplete gamma function

Beta complete and incomplete beta function

PolyGamma polygamma function

LogGamma logarithm of gamma function

Integer-Oriented Functions

Factorial (!)  ▪  Factorial2 (!!)  ▪  Pochhammer  ▪  Binomial

Subfactorial  ▪  FactorialPower  ▪  Hyperfactorial

Regularized Functions

GammaRegularized  ▪  BetaRegularized

Inverse Functions

InverseGammaRegularized  ▪  InverseBetaRegularized

Generalized Functions

BarnesG  ▪  LogBarnesG