On extensions of two results due to Ramanujan

2014/01/15 by Y. S. Kim, A. K. Rathie, Kim, Y. S. +4
Mathematics · #33C15 #33C20 #Advanced Mathematical Identities #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #math.CV #msc:33C15 #msc:33C20

paper · pdf · doi:10.48550/arxiv.1401.3636

7 pages

arxiv created 2014/01/15 · openalex publication_date 2014/01/15 · arxiv updated 2014/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Phi(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 in Kim et al. [Two results for the terminating 3F2(2) with applications, Bull. Korean Math. Soc. 49 (2012) pp. 621633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

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