New representation of gauss hypergeometric function via finite-part integration

Abstract

Finite-part integration is a recently introduced method of evaluating well-defined convergent integrals in the form of Stietjes transform using the finite part of divergent integrals. The divergent integral is induced by expanding the kernel and performing term by term integration. The integral representation of Gauss hypergeometric function resembling the form Stieltjes transform will be evaluated by the method of finite-part integration and will produce a new representation of a specific Gauss hypergeometric function.