On a modified beta function and some applications

摘要

In this work, we study the modified beta function B12(x;a,b)=∫1/2x(1-v)a-1vb-1dv,x∈(0,1) that appeared in Marus˘ić and Bajzer’s solution [M. Marus˘ić, Z˘. Bajzer, Generalized two-parameter equation of growth, J. Math. Anal. Appl. 179 (1993) 446–462] of the generalized two-parameter equation of tumor growth y′ = ayμ + byν. In particular, we provide methods for computing this function for special values of the function’s parameters. Some analytic solutions of the generalized two-parameter growth equation are obtained.