Two associated hypergeometric functions arising from finite part integration

Abstract

In this work, we consider the finite part integral and its complex integral representation to evaluate an integral representation of the generalized hypergeometric function. The result is a new representation of a generalized linear hypergeometric function in terms of two associated quadratic hypergeometric functions with relaxed restrictions as compared to its integral representation. With this new representation, we give two examples to show how it can be used to produce a new relationship and to give a new representation for the Wilson polynomial.