We define a series $\mathcal{F}_{M,N}$ as a certain generalization of $q$-hypergeometric functions. We also study the system of $q$-difference nonlinear equations which admits particular solutions in terms of $\mathcal{F}_{N,M}$. The function $\mathcal{F}_{N,M}$ is a common generalization of $q$-Appell-Lauricella function $\varphi_D$ and the generalized $q$-hypergeometric function ${}_{N+1}\varphi_N$. We construct a Pfaffian system which the function $\mathcal{F}_{N,M}$ satisfies. We derive from the Pfaffian system a monodromy preserving deformation which admits particular solutions in terms of $\mathcal{F}_{N,M}$. In this talk, we will introduce the function $\mathcal{F}_{N,M}$ and its fundamental properties and the system derived from a Pfaffian system which $\mathcal{F}_{M,N}$ satisfies.

(This seminar was held on zoom.)