Definition:Beta Function/Definition 2

Definition
The beta function $\Beta: \C \times \C \to \C$ is defined for $\map \Re x, \map \Re y > 0$ as:
 * $\ds \map \Beta {x, y} := 2 \int_0^{\pi / 2} \paren {\sin \theta}^{2 x - 1} \paren {\cos \theta}^{2 y - 1} \rd \theta$

Also see

 * Equivalence of Definitions of Beta Function