Definition:Hypergeometric Function/Gaussian

Definition
The Gaussian Hypergeometric Function is a hypergeometric function, given for $\left\vert z \right\vert < 1$ by:


 * $\displaystyle {}_2 \operatorname F_1 \left({ {a, b} \atop c } \, \middle \vert {\, z}\right) = \sum_{n \mathop \ge 0} \dfrac { a^{\overline n} b^{\overline n} } { c^{\overline n} } \dfrac {z^n} {n!}$

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.