gamma function

Etymology
The function itself was initially defined as an integral (in modern representation, $$\textstyle\Gamma(x)=\int_0^\infty e^{-t}t^{x-1}dt$$) for positive real x by Swiss mathematician in 1730. The name derives from the notation, Γ(x), which was introduced by (1752—1833) (he referred to it, however, as the Eulerian integral of the second kind). Both Euler's integral and Legendre's notation shift the argument with respect to the factorial, so that for integer n>0, Γ(n) = (n−1)!. preferred π(x), with no shift, but Legendre's notation prevailed. Generalisation to non-integer negative and to complex numbers was achieved by analytic continuation.

Noun

 * 1)  A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers.
 * 2) * 2002, M. Aslam Chaudhry, Syed M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall / CRC Press, page 2,
 * In particular, the exponential, circular, and hyperbolic functions are rational combinations of gamma functions.
 * In particular, the exponential, circular, and hyperbolic functions are rational combinations of gamma functions.

Translations

 * French: fonction gamma
 * German: Gammafunktion
 * Hungarian: gamma-függvény
 * Italian: funzione Gamma, funzione Gamma di Eulero
 * Japanese: ガンマ関数
 * Persian: تابع گاما
 * Polish: funkcja gamma
 * Russian:
 * Swedish:, Eulers gammafunktion
 * Turkish: gama fonksiyonu