# Gamma Function

In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if n is a positive integer:

The gamma function is defined for all complex numbers except the non-positive integers. For complex numbers with a positive real part, it is defined via an improper integral that converges:

This integral function is extended by analytic continuation to all complex numbers except the non-positive integers (where the function has simple poles), yielding the meromorphic function we call the gamma function.

The gamma function is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics.

### Other articles related to "gamma function, gamma, gamma functions, function, functions":

Greek Letters Used In Mathematics, Science, And Engineering - Concepts Represented By A Greek Letter - Γγ (gamma)
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... The duplication formula and the multiplication theorem for the gamma function are the prototypical examples ... The duplication formula for the gamma function is It is also called the Legendre duplication formula or Legendre relation, in honor of Adrien-Marie Legendre ... The multiplication theorem for the gamma functions can be understood to be a special case, for the trivial character, of the Chowla–Selberg formula ...
Gamma Function - History - Reference Tables and Software
... Although the gamma function can be calculated virtually as easily as any mathematically simpler function with a modern computer—even with a programmable pocket calculator—this was of course not ... mathematicians relied on hand-made tables in the case of the gamma function, notably a table computed by Gauss in 1813 and one computed by Legendre in 1825 ... Tables of complex values of the gamma function, as well as hand-drawn graphs, were given in Tables of Higher Functions by Jahnke and Emde, first published in ...
Multivariate Gamma Function
... In mathematics, the multivariate gamma function, Γp(·), is a generalization of the gamma function ... statistics, appearing in the probability density function of the Wishart and inverse Wishart distributions ...

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