SOME SUMMATION FORMULAS FOR THE HYPERGEOMETRIC SERIES r+2Fr+1( 1 2 )

Authors : Y. S. Kim, A. K. Rathie, U. P, - -, R. B. Paris

Pages : 281-287

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Publication Date : 2013-03-01

Article Type : Research Paper

Abstract :The aim of this paper is to obtain explicit expressions of the generalizedhypergeometric functionr+2 F r+1 a, b, insert ignore into journalissuearticles values(a + b + j + 1); insert ignore into journalissuearticles values(f r + m r ); insert ignore into journalissuearticles values(f r ); ; for j = 0, ±1, . . . , ±5, where r pairs of numeratorial and denominatorialparameters differ by positive integers mr . The results are derived withthe help of an expansion in terms of a finite sum ofF insert ignore into journalissuearticles values( ); functions anda generalization of Gauss’ second summation theorem due to Lavoie etal. [J. Comput. Appl. Math. 72, 293–300 insert ignore into journalissuearticles values(1996);]. Some special andlimiting cases are also given.
Keywords : Generalized hypergeometric series, Generalized Gauss summation theorem