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arXiv · 2412.02281

Explicit evaluation of the $q$-Stokes matrices for certain confluent hypergeometric $q$-difference equations

Jinghong Lin·Yiming Ma·Xiaomeng Xu
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Abstract

We prove a connection formula for the basic hypergeomtric function ${}_n\varphi_{n-1}\left( a_1,...,a_{n-1},0; b_1,...,b_{n-1} ; q, z\right)$ by using the $q$-Borel resummation. As an application, we compute $q$-Stokes matrices of a special confluent hypergeometric $q$-difference system with an irregular singularity. We show that by letting $q\rightarrow 1$, the $q$-Stokes matrices recover the known expressions of the Stokes matrices of the corresponding confluent hypergeometric differential system.

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Jinghong Lin, Yiming Ma, Xiaomeng Xu. 2024-12-03. Explicit evaluation of the $q$-Stokes matrices for certain confluent hypergeometric $q$-difference equations. https://arxiv.org/abs/2412.02281

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