NOTE ON THE CLASSICAL WATSON'S THEOREM FOR THE SERIES 3F2

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 4,  2013, pp.701-706
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.4.701
Title & Authors
NOTE ON THE CLASSICAL WATSON'S THEOREM FOR THE SERIES 3F2
Choi, Junesang; Agarwal, P.;

Abstract
Summation theorems for hypergeometric series $\small{_2F_1}$ and generalized hypergeometric series $\small{_pF_q}$ play important roles in themselves and their diverse applications. Some summation theorems for $\small{_2F_1}$ and $\small{_pF_q}$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $\small{_3F_2}$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].
Keywords
Gamma function and its Legendre duplication formula;Gauss's hypergeometric functions $\small{_2F_1}$;Euler's integral formula for $\small{_2F_1}$;classical Watson's theorem for $\small{_3F_2}$;Gauss's summation theorem and second summation theorem for $\small{_2F_1}$;
Language
English
Cited by
References
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