Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 17/Some Important Results

Some Important Results

$17.3$: Commutativity of Parameters of Beta Function

$17.4$: Beta Function: Definition 2

$17.5$: Beta Function as Integeral of $\dfrac {t^{x - 1} } {\paren {1 + t}^{x + y} }$

$17.6$: Beta Function as Integral of $\dfrac {t^{x - 1} \paren {1 - t}^{y - 1} } {\paren {r + t}^{x + y} }$