Familles fuchsiennes d'\'equations aux (q-)diff\'erences et confluence

TL;DR

This paper introduces a unified method for solving families of fuchsian systems across differential, difference, and q-difference equations, and explores their confluence properties.

Contribution

It presents a novel approach that unifies various types of equations and analyzes their confluence behavior within a single framework.

Findings

Unified method for solving fuchsian systems across different operators

Analysis of confluence phenomena in these families

Generalization of differential, difference, and q-difference cases

Abstract

In a first part, we give a method for solving a family of fuchsian systems of operators of pseudo-derivations associated to a family of homographies with two parameters which unify and generalize the differential, the difference and the $q$-difference cases. In a second part, we study the problems of confluence related to these families.