# Beta-function

From Encyclopedia of Mathematics

*-function, Euler -function, Euler integral of the first kind*

A function of two variables and which, for , is defined by the equation

(*) |

The values of the beta-function for various values of the parameters and are connected by the following relationships:

The following formula is valid:

If and are complex, the integral (*) converges if and . The beta-function can be expressed by the gamma-function:

**How to Cite This Entry:**

Beta-function.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Beta-function&oldid=14450

This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article