A class of matrix-valued polynomials generalizing Jacobi Polynomials

TL;DR

This paper introduces a hierarchy of matrix-valued polynomials that extend Jacobi polynomials, characterized by Rodrigues formulas, recurrence relations, and quasi-orthogonality, enriching the theory of special functions.

Contribution

It presents a new class of matrix-valued polynomials generalizing Jacobi polynomials with explicit Rodrigues formulas and structural properties.

Findings

Polynomials are complete and satisfy a two-step recurrence relation.

They exhibit integral inter-relations and quasi-orthogonality.

The hierarchy extends classical Jacobi polynomials to matrix-valued cases.

Abstract

A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations.