Simple bounds for the extreme zeroes of Jacobi polynomials

TL;DR

This paper introduces simple and easy-to-use bounds for the extreme zeroes of Jacobi polynomials, providing results that are comparable to the best known bounds despite their elementary derivation.

Contribution

It presents new, straightforward bounds for the extreme zeroes of Jacobi polynomials, enhancing usability without sacrificing accuracy.

Findings

Bounds are simple and easy to apply.

Lower bounds for Gegenbauer polynomial zeroes are competitive with existing results.

Elementary approach simplifies the derivation process.

Abstract

Some new bounds for the extreme zeroes of Jacobi polynomials are obtained with an elementary approach. A feature of these bounds is their simple forms, which make them easy to work with. Despite their simplicity, our lower bounds for the largest zeroes of Gegenbauer polynomials are compatible with some of the best hitherto known results.