Extracting new representation of the hypergeometric function using finite part integration

Abstract

Finite part integration is a technique in evaluating convergent integrals by means of introducing a divergence. This is done by expanding the kernel and performing a term by term integration. Currently, the method is viable in evaluating integrals of the form of the generalized Stietljes transform. In this paper, we took advantage of the fact that the hypergeometric function is a Stietljes function given the appropriate conditions. Finite part integration is used to evaluate the Stieltjes integral representation and find a new representation of a specific hypergeometric function.