Kampé de Fériet function reduction formula via finite-part integration

Abstract

Finite-part integration is a method of evaluating well-defined convergent integrals using the finite part of divergent integrals. In this paper, a Stieltjes integral representation of the Gauss hypergeometric function is evaluated using the method of finite part integration. It is demonstrated that finite part integration leads to a new reduction formula of the Kampé de Fériet function.