ON AN EXTENSION OF KUMMER-TYPE II TRANSFORMATION

Yıl 2014, Cilt: 4 Sayı: 1, 80 - 85, 01.06.2014

Medhat A. Rakha Arjun K. Rathie

Öz

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.

Anahtar Kelimeler

Generalized Hypergeometric Series, Kummer’s type I and II transformations

Kaynakça

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