\begin{definition}[Definition:Hypergeometric Function]
A '''hypergeometric function''' is an infinite series power series defined as:
:$\ds {}_m \operatorname F_n \left({ {a_1, \ldots, a_m} \atop {b_1, \ldots, b_n} } \, \middle \vert {\, z}\right) := \sum_{k \mathop \ge 0} \dfrac { {a_1}^{\overline k} \cdots {a_m}^{\overline k} } { {b_1}^{\overline k} \cdots {b_n}^{\overline k} } \dfrac {z^k} {k!}$
where $x^{\overline k}$ denotes the $k$th rising factorial power of $x$.
\end{definition}