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We derive extensions of the classical summation theorems of Kummer and Watson for the generalized hypergeometric series where r pairs of numeratorial and denominatorial parameters differ by positive integers. The results are obtained with the help of a generalization of Kummer’s second summation theorem for the 2F1 series given recently by Rakha and Rathie [Integral Transforms and Special Functions, 22, 823–840 (2011)] together with generalizations of the Euler transformations for the r+2Fr+1(z) function. A few interesting special cases are also presented.

Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences