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arXiv · 2402.14358

Jackson integral representation for a multiple $q$-hypergeometric series and an extension of the $q$-Riemann-Papperitz system

Takahiko Nobukawa
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Abstract

We give a Jackson integral representation for Kajihara's $q$-hypergeometric series $W^{M,2}$. We construct a $q$-difference system that corresponds to this integral. This system is an extension of the variant of $q$-hypergeometric equation of degree three, defined by Hatano-Matsunawa-Sato-Takemura. We show that this system includes the $q$-Appell-Lauricella system as a degeneration.

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Takahiko Nobukawa. 2024-02-22. Jackson integral representation for a multiple $q$-hypergeometric series and an extension of the $q$-Riemann-Papperitz system. https://arxiv.org/abs/2402.14358

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