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

TL;DR

This paper explores the connection problem for a specific system of linear q-difference equations, providing formulas that unify and extend known results for q-hypergeometric functions.

Contribution

It introduces a new example of solutions to the connection problem for a particular q-difference system, encompassing q-Lauricella and q-Gauss hypergeometric functions as special cases.

Findings

Derived connection formulas for q-Lauricella hypergeometric functions

Extended connection formulas to q-generalized hypergeometric functions

Unified different hypergeometric functions within a common framework

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.