Jackson integral representation for a multiple $q$-hypergeometric series and an extension of the $q$-Riemann-Papperitz system
Classical Analysis and ODEs
2025-10-21 v3
Abstract
We give a Jackson integral representation for Kajihara's -hypergeometric series . We construct a -difference system that corresponds to this integral. This system is an extension of the variant of -hypergeometric equation of degree three, defined by Hatano-Matsunawa-Sato-Takemura. We show that this system includes the -Appell-Lauricella system as a degeneration.
Keywords
Cite
@article{arxiv.2402.14358,
title = {Jackson integral representation for a multiple $q$-hypergeometric series and an extension of the $q$-Riemann-Papperitz system},
author = {Takahiko Nobukawa},
journal= {arXiv preprint arXiv:2402.14358},
year = {2025}
}
Comments
42 pages. Discussions on convergences of multiple series and changes of limits are added in Appendix