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.

Read more about Gamma Function: Motivation, Approximations, Applications, History

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

... the confinement factor of an optical mode in a waveguide the

**gamma function**, a generalization of the factorial the upper incomplete

**gamma function**the ...

... a Euclidean ball of radius R in n-dimensional Euclidean space is where Γ is Leonhard Euler's

**gamma function**... Using explicit formulas for particular values of the

**gamma function**at the integers and half integers gives formulas for the volume of a unit ball that do not require an evaluation of the

**gamma**...

**Gamma Function**-Legendre Function

... 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 ...

**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 ...

### Famous quotes containing the word function:

“Morality and its victim, the mother—what a terrible picture! Is there indeed anything more terrible, more criminal, than our glorified sacred *function* of motherhood?”

—Emma Goldman (1869–1940)