\begin{definition}[Definition:Gaussian Hypergeometric Function]
The '''Gaussian Hypergeometric Function''' is a hypergeometric function, given for $\size z < 1$ by:
:$\ds {}_2 \map {F_1} {a, b; c; z} = \sum_{n \mathop = 0}^\infty \dfrac {a^{\overline n} b^{\overline n} } {c^{\overline n} } \dfrac {z^n} {n!}$
where $x^{\overline n}$ denotes the $n$th rising factorial power of $x$.
\end{definition}