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.

Certain transformation and summation formulas for generalized hypergeometric series with integral parameter differences are derived.