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Keywords = curious summations

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16 pages, 260 KB  
Article
On a Reduction Formula for a Kind of Double q-Integrals
by Zhi-Guo Liu
Symmetry 2016, 8(6), 44; https://doi.org/10.3390/sym8060044 - 8 Jun 2016
Cited by 8 | Viewed by 4799
Abstract
Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us [...] Read more.
Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us to prove a general q-beta integral formula including the Askey–Wilson integral formula as a special case. Using this double q-integral formula and the theory of q-partial differential equations, we derive a general q-beta integral formula, which includes the Nassrallah–Rahman integral as a special case. Our evaluation does not require the orthogonality relation for the q-Hermite polynomials and the Askey–Wilson integral formula. Full article
(This article belongs to the Special Issue Symmetry in Orthogonal Polynomials)
7 pages, 144 KB  
Article
New Curious Bilateral q-Series Identities
by Frédéric Jouhet and Michael J. Schlosser
Axioms 2012, 1(3), 365-371; https://doi.org/10.3390/axioms1030365 - 31 Oct 2012
Cited by 2 | Viewed by 6092
Abstract
By applying a classical method, already employed by Cauchy, to a terminating curious summation by one of the authors, a new curious bilateral q-series identity is derived. We also apply the same method to a quadratic summation by Gessel and Stanton, and to [...] Read more.
By applying a classical method, already employed by Cauchy, to a terminating curious summation by one of the authors, a new curious bilateral q-series identity is derived. We also apply the same method to a quadratic summation by Gessel and Stanton, and to a cubic summation by Gasper, respectively, to derive a bilateral quadratic and a bilateral cubic summation formula. Full article
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