# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 17

## Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 17

Published $\text {1968}$.

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## $17 \quad$ The Beta Function

### Definition of the Beta Function $\map \Beta {n, m}$

$17.1$: Beta Function: Definition 1

### Relationship of Beta Function to Gamma Function

$17.2$: Beta Function: Definition 3

### 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 $\dfrac {t^{x - 1} \paren {1 - t}^{y - 1} } {\paren {r + t}^{x + y} }$

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