A Generalised Kummer-Type Transformation for the pFp(x) Hypergeometric Function

Abstract

AbstractIn a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p = 1.