An alternative summation formula for the hypergeometric series p+2Fp+1(1) with integral parameter differences

R. B. Paris

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    Abstract

    We obtain a summation formula for the hypergeometric series of unit argument p+2Fp+1 with p pairs of numeratorial and denominatorial parameters differing by positive integers. This summation formula is an alternative representation to that presented by Miller and Paris [Rocky Mountain J. Math. 43 (1) (2013), 291{327] and involves a p-fold sum with coeffcients that contain only ratios of Pochhammer symbols. The case when one of the parameters is a negative integer is also considered.
    Original languageEnglish
    Pages (from-to)685-692
    Number of pages8
    JournalApplied Mathematical Sciences
    Volume15
    Issue number14
    Early online date25 Nov 2021
    DOIs
    Publication statusPublished - 25 Nov 2021

    Keywords

    • Generalised hypergeometric function
    • Summation formulas at unit argument

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