On extensions of two results due to Ramanujan

Authors

YONG SUP KIM
ARJUNKUMAR RATHIE
RICHARD B. PARIS

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.

DOI

10.3906/mat-1909-59

Keywords

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

First Page

348

Last Page

355

Recommended Citation

KIM, Y. S, RATHIE, A, & PARIS, R. B (2020). On extensions of two results due to Ramanujan. Turkish Journal of Mathematics 44 (2): 348-355. https://doi.org/10.3906/mat-1909-59