A remark on the q-hypergeometric integral Bailey pair and the solution to the star-triangle equation

TL;DR

This paper generalizes a recent q-hypergeometric integral Bailey pair and uses it to construct the star-triangle relation, advancing the understanding of integrable models in mathematical physics.

Contribution

It reformulates the q-hypergeometric Bailey pair in a general form and derives the star-triangle relation using this framework.

Findings

Reformulation of the q-hypergeometric integral Bailey pair

Construction of the star-triangle relation from the Bailey pair

Connection between Bailey pairs and integrable models

Abstract

We rewrite the recently constructed q-hypergeometric integral Bailey pair in a general form. Then with the help of the Bailey pair and $q$-beta hypergeometric sum-integral, we construct the star-triangle relation.