ABSTRACT
The incomplete beta function and the incomplete beta function ratio are defined bv
respectively. The incomplete beta function has the simple relation ship
where (z)i = z(z + 1) • • • (z + i — 1) denotes the ascending factorial. The properties of the Gauss hypergeometric function are well estab lished in the literature; see, for example, Section 9.1 of Gradshteyn and Ryzhik (2000). The properties of the incomplete beta function (or equivalently, the incomplete beta function ratio) can thus be de duced easily using (II. 1). In this section we provide a comprehensive list of integral representations, series expansions, recurrence formu las, continued fractions, approximations, inequalities and closed form expressions.
