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# 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 :

${}_{2}F_{1}(a,b;\,c\,;z)=\sum_{{n=0}}^{{\infty}}\frac{(a)_{n}(b)_{n}}{(c)_{{n}% }n!}z^{n}.$ |

Defines:

Gauss hypergeometric function

Keywords:

hypergeometric, Gauss

Related:

TableOfMittagLefflerPartialFractionExpansions

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

33C05*no label found*

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## Attached Articles

integral representation of the hypergeometric function by rspuzio

Barnes' integral representation of the hypergeometric function by rspuzio

differential-difference equations for hypergeometric function by rspuzio

global characterization of hypergeometric function by rspuzio

special cases of hypergeometric function by pahio

Barnes' integral representation of the hypergeometric function by rspuzio

differential-difference equations for hypergeometric function by rspuzio

global characterization of hypergeometric function by rspuzio

special cases of hypergeometric function by pahio