# Definition:Gaussian Hypergeometric Function

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## Definition

The **Gaussian Hypergeometric Function** is a hypergeometric function, given for $\size z < 1$ by:

- $\displaystyle {}_2 \map {F_1} {a, b; c; z} = \sum_{n \mathop = 0}^\infty \dfrac { a^{\overline n} b^{\overline n} } { c^{\overline n} } \dfrac {z^n} {n!}$

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**.

## Also see

- Results about
**Gaussian Hypergeometric Function**can be found here.

## Source of Name

This entry was named for Carl Friedrich Gauss.

## Sources

- 1920: E.T. Whittaker and G.N. Watson:
*A Course of Modern Analysis*(3rd ed.): $14.1$: The hypergeometric series - 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 31$: Hypergeometric Functions: $31.2$