Connection Problem for an Extension of $q$-Hypergeometric Systems

Takahiko Nobukawa

Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Abstract: We give an example of solutions of the connection problem associated with a certain system of linear $q$-difference equations recently introduced by Park. The result contains a connection formulas of the $q$-Lauricella hypergeometric function $\varphi_{D}$ and those of the $q$-generalized hypergeometric function ${}_{N+1}\varphi_{N}$ as special cases.

Keywords: $q$-difference equations, $q$-hypergeometric series, connection matrices, Yang–Baxter equation.

MSC: 33D70, 39A13

Received: March 19, 2021; in final form October 14, 2022; Published online October 21, 2022

Language: English

DOI: 10.3842/SIGMA.2022.080

Bibliographic databases:

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ArXiv: 2102.09175