KUMMER’S THEOREM AND ITS CONTIGUOUS IDENTITIES
Copyright policy )KUMMER’S THEOREM AND ITS CONTIGUOUS IDENTITIES
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.
33C60, generalized Whipple's summation theorem for ${}_3F_2$, hypergeometric series ${}_2F_1$, Kummer's summation formula for ${}_2F_1$, 33C70, 33C05, 33C65
33C60, generalized Whipple's summation theorem for ${}_3F_2$, hypergeometric series ${}_2F_1$, Kummer's summation formula for ${}_2F_1$, 33C70, 33C05, 33C65
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