# Incomplete beta-function

From Encyclopedia of Mathematics

The function defined by the formula

where

is the beta-function. If is an integer, then

Series representation:

Continued fraction representation:

where

Asymptotic representation for large and :

where

Asymptotic representation for large and bounded :

where

Connection with the hypergeometric function:

Recurrence relations:

#### References

[1] | M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1973) |

[2] | K. Pearson, "Tables of the incomplete beta-function" , Cambridge Univ. Press (1932) |

**How to Cite This Entry:**

Incomplete beta-function.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Incomplete_beta-function&oldid=16063

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