In 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.
Miller, A. R., & Paris, R. B. (2012). A generalised Kummer-type transformation for the pFp(x) hypergeometric function. Canadian Mathematical Bulletin, 55, 571-578. https://doi.org/10.4153/CMB-2011-095-6