Jointly orthogonal polynomials

TL;DR

This paper explores the extension of classical orthogonal polynomial theory to multiple inner products, including examples like Lamé and Heine-Stieltjes polynomials, broadening the scope of orthogonal polynomial research.

Contribution

It introduces a framework for orthogonal polynomials with respect to multiple inner products, expanding classical theory to new polynomial families.

Findings

Extended orthogonal polynomial theory to multiple inner products

Included examples such as Lamé and Heine-Stieltjes polynomials

Provided foundational insights for future research in this area

Abstract

The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lam\'e and Heine-Stieltjes polynomials.