hypergeometric functionHypergeometricFunction2004-07-05 08:19:552006-12-12 23:52:54DefinitionGauss hypergeometric functionhypergeometricGauss% this is the default PlanetMath preamble. as your knowledge
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% define commands hereLet $(a,b,c)$ 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 \emph{Gauss hypergeometric function}, $_{2}F_{1}$, is then defined by the following power series expansion : $$_2F_1(a,b;\,c\,;z)=\sum_{n=0}^{\infty} \frac{(a)_n(b)_n}{(c)_{n}n!}z^n.$$