Definition:Hypergeometric Function

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Definition

A hypergeometric function is an infinite series power series defined as:

$\displaystyle {}_m \operatorname F_n \left({ {a_1, \ldots, a_m} \atop {b_1, \ldots, b_n} } \, \middle \vert {\, z}\right) := \sum_{k \mathop \ge 0} \dfrac { {a_1}^{\overline k} \cdots {a_m}^{\overline k} } { {b_1}^{\overline k} \cdots {b_n}^{\overline k} } \dfrac {z^k} {k!}$

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


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