Nonterminating transformations and summations associated with some q-Mellin–Barnes integrals

In many cases one may encounter an integral which is of q-Mellin–Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interesting q-Mellin–Barnes integrals and using them we derive transform...

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Bibliographic Details
Published in:Advances in applied mathematics Vol. 147; p. 102517
Main Authors: Cohl, Howard S., Costas-Santos, Roberto S.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2023
Subjects:
Askey–Wilson moments
Askey–Wilson polynomials
Integral representations
Nonterminating basic hypergeometric functions
Nonterminating summations
Nonterminating transformations
q-calculus
q-Mellin–Barnes integrals
Askey–Wilson moments
Integral representations
Askey–Wilson polynomials
33D60
Nonterminating basic hypergeometric functions
Nonterminating transformations
q-Mellin–Barnes integrals
33D15
q-calculus
Nonterminating summations
ISSN:0196-8858, 1090-2074
Online Access:Get full text
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Summary:In many cases one may encounter an integral which is of q-Mellin–Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interesting q-Mellin–Barnes integrals and using them we derive transformation and summation formulas for nonterminating basic hypergeometric functions. The cases which we treat include ratios of theta functions, the Askey–Wilson moments, nonterminating well-poised ϕ23, nonterminating very-well-poised W45, W78, products of two nonterminating ϕ12's, square of a nonterminating well-poised ϕ12, a nonterminating W910, two nonterminating W1112's and several nonterminating summations which arise from the Askey–Roy and Gasper integrals.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2023.102517