# Category:Gaussian Hypergeometric Function

This category contains results about Gaussian Hypergeometric Function.

The Gaussian hypergeometric function is an instance of a generalized hypergeometric function, given for $\size z < 1$ by:

 $\ds \map F {a, b; c; z}$ $:=$ $\ds \sum_{n \mathop = 0}^\infty \dfrac {a^{\overline n} b^{\overline n} } {c^{\overline n} } \dfrac {z^n} {n!}$ where $x^{\overline n}$ denotes the $n$th rising factorial power of $z$ $\ds$ $=$ $\ds 1 + \dfrac {a b} {1! \, c} z + \dfrac {a \paren {a + 1} b \paren {b + 1} } {2! \, c \paren {c + 1} } z^2 + \dfrac {a \paren {a + 1} \paren {a + 2} b \paren {b + 1} \paren {b + 2} } {3! \, c \paren {c + 1} \paren {c + 2} } z^3 + \cdots$

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Gaussian Hypergeometric Function"

The following 13 pages are in this category, out of 13 total.