Definition:Hypergeometric Function/Gaussian

Definition
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 $x$.

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