On an extension of kummer-type II transformation

Abstract

In the theory of hypergeometric and generalized hypergeometric series, Kummer’s type I and II transformations play an important role. In this short research paper, we aim to establish the explicit expression of e? x/2 2F2 [a, d + n; x 2a + n, d;] for n = 3. For n = 0, we have the well known Kummer’s second transformation. For n = 1, the result was established by Rathie and Pogany [12] and later on by Choi and Rathie[2]. For n = 2, the result was recently established by Rakha, et al. [10]. The result is derived with the help of Kummer’s second transformation and its contiguous results recently obtained by Kim, et. al.[4]. The result established in this short research paper is simple, interesting, easily established and may be potentially useful.