We solve the connection problem of a certain system of linear $q$-difference equations recently introduced by K. Park. The result contains the 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. Our result gives a simultaneous extension of them.
New Estimations for Sturm-Liouville Problems in Difference Equations
Spectral types of linear $q$-difference equations and $q$-analog of middle convolution
A note on the connection problem of some special Painlevé V functions
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