On a q-Deformation of the Discrete Painlev\'e I Equation and q-Orthogonal Polynomials

TL;DR

This paper introduces a q-analog of the discrete Painlevé I equation and demonstrates its realization through q-orthogonal polynomials, expanding the understanding of integrable systems and special functions.

Contribution

It presents a novel q-deformation of the discrete Painlevé I equation and links it to q-orthogonal polynomials, providing new insights into their structure.

Findings

Established a q-analog of the discrete Painlevé I equation

Connected the q-analog to specific q-orthogonal polynomials

Provided a framework for further exploration of q-deformed integrable systems

Abstract

I present a $q$-analog of the discrete Painlev\'e I equation, and a special realization of it in terms of $q$-orthogonal polynomials.