### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 080, 21 pages      arXiv:2102.09175      https://doi.org/10.3842/SIGMA.2022.080

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

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

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

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.

Key words: $q$-difference equations; $q$-hypergeometric series; connection matrices; Yang-Baxter equation.

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