# 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 :

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

The Gauss hypergeometric function, ${}_{2}F_{1}$, is then defined by the following power series expansion :

 ${}_{2}F_{1}(a,b;\,c\,;z)=\sum_{n=0}^{\infty}\frac{(a)_{n}(b)_{n}}{(c)_{n}n!}z^% {n}.$
Title hypergeometric function HypergeometricFunction 2013-03-22 14:27:48 2013-03-22 14:27:48 rspuzio (6075) rspuzio (6075) 9 rspuzio (6075) Definition msc 33C05 TableOfMittagLefflerPartialFractionExpansions Gauss hypergeometric function