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

Year 2013, Volume: 42 Issue: 3, 281 - 287, 01.03.2013

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

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

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

Abstract

References

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