Sum of a double series

Sharma, B. L.

doi:10.1090/S0002-9939-1975-0387678-1

Sum of a double series
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by B. L. Sharma PDF

Proc. Amer. Math. Soc. 52 (1975), 136-138 Request permission

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 $_4{F_3}(1)$, \[ _4{F_3}\left [ {\begin {array}{*{20}{c}} {\alpha ,\beta - \alpha ,1/2\rho ,1/2\rho + 1/2;1} \\ {1/2\beta ,1/2(1 + \beta ),1 + \rho ;} \\ \end {array} } \right ] = \tfrac {{\Gamma (\beta - \rho - \alpha )\Gamma (\beta )}} {{\Gamma (\beta - \rho )\Gamma (\beta - \alpha )}},\] 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].

References

Fonctions hypergéométriques et hypersphériques, polynômes d’Hermite

Some identities involving generalised hypergeometric series

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