A reduction formula for the hypergeometric function 2F2(β, 1/2; β+σ, −1/2; z) using finite-part integrals

Abstract

The hypergeometric function ₂F₂(β, 1/2; β+σ, −1/2; z) is shown to assume a finite-part integral representation, from which a reduction formula for ₂F₂ is obtained in terms of the confluent hypergeometric function ₁F₁. The result demonstrates how finite-part integrals can be used to uncover new relationships among the special functions of mathematical physics.