Extensions of certain classical summation theorems for the series 2F1, 3F2, and 4F 3 with applications in Ramanujan's summations

Abstract

Motivated by the extension of classical Gauss's summation theorem for the series 2F1 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 2F 1, Watson, Dixon and Whipple for the series 3F 2, and a few other hypergeometric identities for the series 3F2 and 4F3. 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. Copyright © 2010 Yong Sup Kim et al.