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

Objective & Hypothesis:The aim of this paper is to obtain explicit expressions of the generalizedhypergeometric functionr+2 F r+1 a, b, (a + b + j + 1),(f r + m r ) (f r ) ; for j = 0, ±1, . . . , ±5, where r pairs of numeratorial and denominatorialparameters differ by positive integers mr .

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Key Findings & Data:Math. 72, 293–300 (1996)].

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Conclusion & Impact:Some special andlimiting cases are also given.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Generalized hypergeometric series · Generalized Gauss summation theorem

Abstract

The aim of this paper is to obtain explicit expressions of the generalizedhypergeometric functionr+2 F r+1 a, b, (a + b + j + 1),(f r + m r ) (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 ( ) functions anda generalization of Gauss’ second summation theorem due to Lavoie etal. [J. Comput. Appl. Math. 72, 293–300 (1996)]. Some special andlimiting cases are also given.

Keywords

Generalized hypergeometric series Generalized Gauss summation theorem

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Cite This Article

Kim, Y. S., Rathie, A. K., P, U., -, -., Paris, R. B. (2013). SOME SUMMATION FORMULAS FOR THE HYPERGEOMETRIC SERIES r+2Fr+1( 1 2 ). Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 3, 281–287. https://ajindex.com/articles/669605

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