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

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.