Applications of generalized Kummer's summation theorem for the series ${}_{2}F_{1}$

摘要

The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series ${}_{3}F_{2}$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series ${}_{2}F_{1}$ obtained earlier by Lavoie, Grondin, and Rathie.