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

Cohl, H. S. and Costas-Santos, R. S.
**Advances in Applied Mathematics**147, June 2023, 102517

## Abstract

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 \({}_2\phi_3\), nonterminating very-well-poised \({}_4W_5\), \({}_7W_8\), products of two nonterminating \({}_1\phi_2\)'s, square of a nonterminating well-poised \({}_1\phi_2\), a nonterminating \({}_9W_{10}\), two nonterminating \({}_{11}W_{12}\)'s and several nonterminating summations which arise from the Askey-Roy and Gasper integrals.

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## BibTeX

@article {MR4566042, AUTHOR={Cohl, H. S. and Costas-Santos, R. S.}, TITLE={Nonterminating transformations and summations associated with some {$q$}-{M}ellin-{B}arnes integrals}, JOURNAL={Adv. in Appl. Math.}, FJOURNAL={Advances in Applied Mathematics}, VOLUME={147}, YEAR={2023}, PAGES={Paper No. 102517}, ISSN={0196-8858}, MRCLASS={33D15 (33D60)}, MRNUMBER={4566042}, DOI={10.1016/j.aam.2023.102517}, URL={https://doi.org/10.1016/j.aam.2023.102517}, }