hypergeometric function

Let $(a,b,c)$ be a triple of complex numbers with $c$ not belonging to the set of negative integers. For a complex number $w$ and a non negative integer $n$, use Pochhammer symbol ${(w)}_n$ , to denote the expression :

$${(w)}_n=w(w+1)\mathrm{\dots }(w+n-1).$$

The Gauss hypergeometric function, ${}_{2}F_1$, is then defined by the following power series expansion :

$${}_{2}F_1(a,b;c;z)=\sum _{n=0}^{\mathrm{\infty }}\frac{{(a)}_n{(b)}_n}{{(c)}_{n}n!}{z}^n.$$

Title	hypergeometric function
Canonical name	HypergeometricFunction
Date of creation	2013-03-22 14:27:48
Last modified on	2013-03-22 14:27:48
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	9
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 33C05
Related topic	TableOfMittagLefflerPartialFractionExpansions
Defines	Gauss hypergeometric function