Definition:Beta Function/Definition 3

Definition

The beta function $\Beta: \C \times \C \to \C$ is defined for $\map \Re x, \map \Re y > 0$ as:

$\map \Beta {x, y} := \dfrac {\map \Gamma x \map \Gamma y} {\map \Gamma {x + y} }$

where $\Gamma$ is the gamma function.

Also see

• Equivalence of Definitions of Beta Function

• Definition:Gamma Function

• Results about the beta function can be found here.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $17.2$: Relationship of Beta Function to Gamma Function
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 17.7 \ (5)$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): beta function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): beta function