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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Sum of a double series


Author: B. L. Sharma
Journal: Proc. Amer. Math. Soc. 52 (1975), 136-138
MSC: Primary 33A30
DOI: https://doi.org/10.1090/S0002-9939-1975-0387678-1
MathSciNet review: 0387678
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Abstract: In this paper we obtain the sum of a double series $ F(1,1)$ and, in a particular case, we get a new formula $ _4{F_3}(1)$,

$\displaystyle _4{F_3}\left[ {\begin{array}{*{20}{c}} {\alpha ,\beta - \alpha ,1... ...- \alpha )\Gamma (\beta )}} {{\Gamma (\beta - \rho )\Gamma (\beta - \alpha )}},$

provided that $ R(\beta - \alpha ) > 0$, $ R(\beta - \rho - \alpha ) > 0$ and $ R(\beta - \rho ) > 0$. If $ \alpha = - n$, the formula reduces to a known result due to Bailey [2].

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0387678-1
Keywords: Double series, Saalschutizian theorem, hypergeometric series of higher order and of two variables, summation formula
Article copyright: © Copyright 1975 American Mathematical Society