English

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 qq-hypergeometric series WM,2W^{M,2}. We construct a qq-difference system that corresponds to this integral. This system is an extension of the variant of qq-hypergeometric equation of degree three, defined by Hatano-Matsunawa-Sato-Takemura. We show that this system includes the qq-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