# Definition:Gaussian Hypergeometric Function

## Definition

The Gaussian Hypergeometric Function is a hypergeometric function, given for $\size z < 1$ by:

$\displaystyle {}_2 \map {F_1} {a, b; c; z} = \sum_{n \mathop = 0}^\infty \dfrac { a^{\overline n} b^{\overline n} } { c^{\overline n} } \dfrac {z^n} {n!}$

where $x^{\overline n}$ denotes the $n$th rising factorial power of $x$.

## Also known as

The Gaussian hypergeometric function is also known as the ordinary hypergeometric function.

## Also see

• Results about Gaussian Hypergeometric Function can be found here.

## Source of Name

This entry was named for Carl Friedrich Gauss.