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 .

REFERENCES:

Pearson, K. (Ed.). Tables of Incomplete Beta Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1968.