On extensions of two results due to Ramanujan

Abstract

The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks thatrelate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derivedwith the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recentlyobtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean MathematicalSociety 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to includeintegral parameter differences