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:
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The following formula is valid:
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If and
are complex, the integral (*) converges if
and
. The beta-function can be expressed by the gamma-function:
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How to Cite This Entry:
Beta-function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Beta-function&oldid=14450
Beta-function. Encyclopedia of Mathematics. URL: http://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