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We define a series $\mathcal{F}_{M,N}$ as a certain generalization of$q$-hypergeometric function. We study its duality and the system of$q$-difference nonlinear equations which admits particular solutions in termsof $\mathcal{F}_{1,M}$.

A certain generalization of $q$-hypergeometric functions and their related monodromy preserving deformation