The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].
Kim, Y. S., Rathie, A. K., & Paris, R. B. (2013). An extension of Saalschütz's summation theorem for the series r+3Fr+2. Integral Transforms and Special Functions, 24(11), 916-921. https://doi.org/10.1080/10652469.2013.777721