KUMMER’S THEOREM AND ITS CONTIGUOUS IDENTITIES

Abstract

Recently Lavoie, Grondin and Rathie obtained ten results closely related to the classical Kummer's theorem as special cases from generalized Whipple's theorem on the sum of a ${}_3F_2$ with unit argument. The aim of this paper is to provide general summation formulas contiguous to the Kummer's theorem by simply using a known integral representation of ${}_2F_1$. As by-product, two classes of summation formulas closely related to the Kummer's theorem were obtained. Some simplified special cases were also given for later easy use.