On extensions of two results due to Ramanujan

Yong Sup Kim*, Arjun Kumar Rathie, Richard Bruce Paris

*Corresponding author for this work

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    The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.
    Original languageEnglish
    Pages (from-to)348-355
    Number of pages8
    JournalTurkish Journal of Mathematics
    Issue number2
    Early online date28 Dec 2019
    Publication statusPublished - 17 Mar 2020


    • Hypergeometric series
    • Ramanujan's sum
    • Sums of Hermite polynomials


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