On a new class of summation formulae involving the Laguerre polynomial

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

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    5 Citations (Scopus)
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    Abstract

    By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form.
    Original languageEnglish
    Pages (from-to)435-444
    Number of pages10
    JournalIntegral Transforms and Special Functions
    Volume23
    Issue number6
    Early online date18 Jul 2011
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Generalized hypergeometric series
    • Generalized Kummer summation theorem
    • Laguerre polynomials

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