Jackson integral representation for a multiple -hypergeometric series and an extension of the -Riemann-Papperitz system
arXiv:2402.14358
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.
42 pages. Discussions on convergences of multiple series and changes of limits are added in Appendix