# Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials

## TL;DR

This paper uses Bethe Ansatz algebraic equations to establish bounds on the zeros of various hypergeometric orthogonal polynomials, connecting algebraic solutions to polynomial zero distributions.

## Contribution

It introduces a novel approach linking Bethe Ansatz solutions to the zero bounds of Askey-Wilson, Wilson, and continuous Hahn polynomials.

## Key findings

- Derived bounds for zeros of hypergeometric orthogonal polynomials
- Connected algebraic Bethe Ansatz solutions to polynomial zero distributions
- Extended results to Askey-Wilson, Wilson, and continuous Hahn families

## Abstract

Via the solutions of systems of algebraic equations of Bethe Ansatz type, we arrive at bounds for the zeros of orthogonal (basic) hypergeometric polynomials belonging to the Askey-Wilson, Wilson and continuous Hahn families.