A NEW PROOF OF THE EXTENDED SAALSCHÜTZ'S SUMMATION THEOREM FOR THE SERIES 4F3 AND ITS APPLICATIONS

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 3,  2013, pp.407-415
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.3.407
Title & Authors
A NEW PROOF OF THE EXTENDED SAALSCHÜTZ'S SUMMATION THEOREM FOR THE SERIES 4F3 AND ITS APPLICATIONS
Choi, Junesang; Rathie, Arjun K.; Chopra, Purnima;

Abstract
Very recently, Rakha and Rathie obtained an extension of the classical Saalsch$\small{\ddot{u}}$tz's summation theorem. Here, in this paper, we first give an elementary proof of the extended Saalsch$\small{\ddot{u}}$tz's summation theorem. By employing it, we next present certain extenstions of Ramanujan's result and another result involving hypergeometric series. The results presented in this paper are simple, interesting and (potentially) useful.
Keywords
Hypergeometric series $\small{_2F_1}$;Generalized hypergeometric series $\small{_pF_q}$;Saalsch$\small{\ddot{u}}$tz's summation theorem and its extension;Ramanujan's formulas;
Language
English
Cited by
1.
An alternative proof of the extended Saalschütz summation theorem for ther+ 3Fr+ 2(1) series with applications, Mathematical Methods in the Applied Sciences, 2015, 38, 18, 4891
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