Clausen's series 3 F 2(1) with integral parameter differences and transformations of the hypergeometric function 2 F 2(x)

Abstract

We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.