Beta Function as Integral of Power of t by Power of 1 minus t over Power of r plus t

From ProofWiki
Jump to: navigation, search

Theorem

$\displaystyle \Beta \left({x, y}\right) := r^y \left({r + 1}\right)^x \int_{\mathop \to 0}^{\mathop \to 1} \frac {t^{x - 1} \left({1 - t}\right)^{y - 1} } {\left({r + t}\right)^{x + y} } \ \mathrm d t$

where $\Beta$ denotes the Beta function.


Proof


Sources