Definition:Beta Function/Definition 2

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:
 * $\displaystyle \Beta \left({x, y}\right) := 2 \int_0^{\pi / 2} \left({\sin \theta}\right)^{2x - 1} \left({\cos \theta}\right)^{2y - 1} \ \mathrm d \theta$

Also see

 * Equivalence of Definitions of Beta Function