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Incomplete beta-function

From Encyclopedia of Mathematics
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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