Properties of Generalized Hypergeometric Function

Theorem
From the, we have:
 * $\ds \map { {}_m \operatorname F_n} { { {a_1, \ldots, a_m} \atop {b_1, \ldots, b_n} } \, \middle \vert \, z} = \sum_{k \mathop = 0}^\infty \dfrac { {a_1}^{\overline k} \cdots {a_m}^{\overline k} } { {b_1}^{\overline k} \cdots {b_n}^{\overline k} } \dfrac {z^k} {k!}$

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

This page gathers together some of the properties of hypergeometric functions.