An alternative proof of the extended Saalschütz summation theorem for the r + 3Fr + 2(1) series with applications

Yong S. Kim, Arjun K. Rathie, Richard B. Paris

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    Abstract

    A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well-known Saalschütz summation formula for a 3F2(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller.
    Original languageEnglish
    Pages (from-to)4891-4900
    Number of pages10
    JournalMathematical Methods in the Applied Sciences
    Volume38
    Issue number18
    Early online date6 Mar 2015
    DOIs
    Publication statusPublished - Dec 2015

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