Regularized Beta Function
The regularized beta function is defined by
 |
where 
is the incomplete
beta function and 
is the (complete)
beta function. The regularized beta function is
sometimes also denoted 
and is
implemented in the Wolfram Language
as BetaRegularized[z,
a, b]. The four-argument version BetaRegularized[z1,
z2, a, b] is equivalent to 
.
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Bailey's theorem