On extensions of two results due to Ramanujan

Yong Sup Kim; Arjun Kumar Rathie; Richard Bruce Paris

doi:10.3906/mat-1909-59

On extensions of two results due to Ramanujan

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

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 language	English
Pages (from-to)	348-355
Number of pages	8
Journal	Turkish Journal of Mathematics
Volume	44
Issue number	2
Early online date	28 Dec 2019
DOIs	https://doi.org/10.3906/mat-1909-59
Publication status	Published - 17 Mar 2020

Keywords

Hypergeometric series
Ramanujan's sum
Sums of Hermite polynomials

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Cite this

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