On certain hypergeometric identities deducible by using beta integral method

TL;DR

This paper demonstrates how to derive eleven new hypergeometric identities using the beta integral method, building on previous transformations and generalizations, with potential applications in mathematical analysis.

Contribution

It introduces eleven new hypergeometric identities derived via the beta integral method, extending previous results with a recent quadratic transformation generalization.

Findings

Derived eleven new hypergeometric identities

Extended previous identities using a recent quadratic transformation

Identified identities that are simple and potentially useful

Abstract

The aim of this research paper is to demonstrate how one can obtain eleven new and interesting hypergeometric identities (in the form of a single result) from the old ones by mainly applying the well known beta integral method which was used successfully and systematically by Krattenthaler and Rao in their well known, very interesting research papers. The results are derived with the help of generalization of a quadratic transformation formula due to Kummer very recently obtained by Kim, et al. . Several identities including one obtained earlier by Krattenthaler and Rao follow special cases of our main findings. The results established in this paper are simple, interesting, easily established and may be potentially useful.