Generalization of two theorems due to Ramanujan

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

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    3 Citations (Scopus)

    Abstract

    The aim in this paper is to provide generalizations of two interesting entries in Ramanujan's notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalizations obtained are derived with the help of expressions for the Gauss hypergeometric function 2 F 1(−n, a; 2a+j; 2) for non-negative integer n and j=0,±1, …,±5 given very recently by Kim et al. [Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), pp. 387–402] and extension of Gauss’ summation theorem available in the literature. Several special cases that are closely related to Ramanujan's results are also given.
    Original languageEnglish
    Pages (from-to)314-323
    Number of pages10
    JournalIntegral Transforms and Special Functions
    Volume24
    Issue number4
    Early online date24 May 2012
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Hypergeometric series
    • Generalized Gauss summation theorem
    • Ramanujan's sum
    • Sums of Hermite polynomials

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