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

Abstract

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 terms of ${\mathcal{F}}_{1,M}$.

12pages