Evaluations of some terminating hypergeometric 2F1(2) series with applications

Yongsup Kim*, Arjun Kumar Rathie, Richard Bruce Paris

*Corresponding author for this work

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    Abstract

    Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).

    Original languageEnglish
    Pages (from-to)2563-2575
    Number of pages13
    JournalTurkish Journal of Mathematics
    Volume42
    Issue number5
    DOIs
    Publication statusPublished - 27 Sep 2018

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