Finite Double Sums of Kampe de Feriet's Hypergeometric Function of Higher Order

Mohammad Idris Qureshi; Deepak Kumar Kabra; Yasmeen

doi:https://doi.org/10.14445/22315373/IJMTT-V33P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 33 | Number 2 | Year 2016 | Article Id. IJMTT-V33P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V33P514

Finite Double Sums of Kampe de Feriet's Hypergeometric Function of Higher Order

Mohammad Idris Qureshi, Deepak Kumar Kabra, Yasmeen

Citation :

Mohammad Idris Qureshi, Deepak Kumar Kabra, Yasmeen, "Finite Double Sums of Kampe de Feriet's Hypergeometric Function of Higher Order," International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 2, pp. 104-111, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V33P514

Abstract

In this paper we obtain four finite double sums of Kamp´e de F´eriet’s double hypergeometric function of higher order using Gauss’s summation theorem. Associated and contiguous relations for Kummer’s confluent hypergeometric function, Gauss’s ordinary hypergeometric function, Saalsch¨utz’s summation theorem, double sums involving Appell, Humbert, Karlsson, Bessel functions, are obtained as special cases of our main double summations.

Keywords

Gauss’s summation theorem, Saalsch¨utz’s summation theorem, Karlsson’s quadruple hypergeometric function, Bessel’s function, Kamp´e de F´eriet’s double hypergeometric function.

References

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