On extensions of two results due to Ramanujan

Authors

YONG SUP KIM
ARJUNKUMAR RATHIE
RICHARD B. PARIS

DOI

10.3906/mat-1909-59

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 $\varphi\left( t\right)$ evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating ${}_3F_2$ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ${}_3F_2$(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.

Keywords

Hypergeometric series, Ramanujan's sum, sums of Hermite polynomials

First Page

348

Last Page

355

Recommended Citation

KIM, YONG SUP; RATHIE, ARJUNKUMAR; and PARIS, RICHARD B. (2020) "On extensions of two results due to Ramanujan," Turkish Journal of Mathematics: Vol. 44: No. 2, Article 1. https://doi.org/10.3906/mat-1909-59
Available at: https://journals.tubitak.gov.tr/math/vol44/iss2/1