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

Yongsup Kim*, Arjun Kumar Rathie, Richard Bruce Paris

*Corresponding author for this work

    Research output: Contribution to journalArticle

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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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    Confluent Hypergeometric Function
    Hypergeometric Series
    Summation Formula
    Integer
    Series
    Evaluation
    Summation
    Arbitrary
    Theorem
    Generalization

    Cite this

    Kim, Yongsup ; Rathie, Arjun Kumar ; Paris, Richard Bruce. / Evaluations of some terminating hypergeometric 2F1(2) series with applications. In: Turkish Journal of Mathematics. 2018 ; Vol. 42, No. 5. pp. 2563-2575.
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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).",
    author = "Yongsup Kim and Rathie, {Arjun Kumar} and Paris, {Richard Bruce}",
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    Evaluations of some terminating hypergeometric 2F1(2) series with applications. / Kim, Yongsup; Rathie, Arjun Kumar; Paris, Richard Bruce.

    In: Turkish Journal of Mathematics, Vol. 42, No. 5, 27.09.2018, p. 2563-2575.

    Research output: Contribution to journalArticle

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    AU - Rathie, Arjun Kumar

    AU - Paris, Richard Bruce

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    Y1 - 2018/9/27

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