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

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

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.

Download

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},
}