Definition:Beta Function/Definition 3

Definition
The Beta Function $\Beta: \C \times \C \to \C$ is defined for $\operatorname{Re} \left({x}\right), \operatorname{Re} \left({y}\right) > 0$ as:
 * $\Beta \left({x, y}\right) := \dfrac {\Gamma \left({x}\right) \Gamma \left({y}\right)} {\Gamma \left({x + y}\right)}$

where $\Gamma$ is the Gamma function.

Also see

 * Equivalence of Definitions of Beta Function


 * Definition:Gamma Function