Extensions of Certain Classical Summation Theorems for the Series F21, F32, and F43 with Applications in Ramanujan's Summations

Abstract EN

Motivated by the extension of classical Gauss's summation theorem for the series F21 given in the literature, the authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series F21, Watson, Dixon and Whipple for the series F32, and a few other hypergeometric identities for the series F32 and F43.

As applications, certain very interesting summations due to Ramanujan have been generalized.

The results derived in this paper are simple, interesting, easily established, and may be useful.