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

TL;DR

This paper introduces a nonlinear q-difference system as a monodromy preserving deformation of a linear equation, exploring its connection to a generalized q-hypergeometric function series.

Contribution

It defines a new q-difference system and investigates its relation to a generalized q-hypergeometric function, extending previous work in the area.

Findings

Established the nonlinear q-difference system as a monodromy preserving deformation.

Linked the system to a generalized q-hypergeometric function series.

Provided foundational results for further study of q-difference equations.

Abstract

We define a nonlinear $q$-difference system $mathcal{P}_{N,(M_-,M_+)}$ as monodromy preserving deformations of a certain linear equation. We study its relation to a series $mathcal{F}_{N,M}$ defined as a certain generalization of $q$-hypergeometric functions.