Hypergeometric solutions to the symmetric q-Painlev\'e equations

TL;DR

This paper constructs hypergeometric solutions for symmetric q-Painlevé equations derived from affine Weyl groups and explores their continuous limits to classical Painlevé equations.

Contribution

It introduces a method to obtain hypergeometric solutions for symmetric q-Painlevé equations via projective reduction from affine Weyl groups.

Findings

Hypergeometric solutions explicitly constructed for symmetric q-Painlevé equations.

Continuous limits connect q-Painlevé solutions to classical Painlevé hypergeometric solutions.

Framework facilitates analysis of integrable systems and special functions.

Abstract

We consider the symmetric q-Painlev\'e equations derived from the birational representation of affine Weyl groups by applying the projective reduction and construct the hypergeometric solutions. Moreover, we discuss continuous limits of the symmetric q-Painlev\'e equations to Painlev\'e equations together with their hypergeometric solutions.