On the Rational Solutions of q-Painlev\'e V Equation

TL;DR

This paper presents an explicit determinant formula for rational solutions of a q-analogue of the Painlevé V equation, utilizing continuous q-Laguerre polynomials, advancing the understanding of special function solutions in q-difference equations.

Contribution

It provides the first explicit determinant formula for rational solutions of the q-Painlevé V equation using continuous q-Laguerre polynomials.

Findings

Explicit determinant formula derived for rational solutions.

Entries of the determinant are continuous q-Laguerre polynomials.

Enhances understanding of special solutions in q-difference Painlevé equations.

Abstract

We give an explicit determinant formula for a class of rational solutions of a q-analogue of the Painlev\'e V equation. The entries of the determinant are given by the continuous q-Laguerre polynomials.