A class of matrix-valued polynomials generalizing Jacobi Polynomials

2008/04/23 by Rodica D. Costin, Costin, Rodica D.
Mathematics · Physics and Astronomy · Computer Science · #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.0804.3739

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.

Related

• Matrix valued polynomials generated by the scalar-type Rodrigues' formulas
• Bispectral Jacobi type polynomials
• Matrix Jacobi Biorthogonal Polynomials via Riemann-Hilbert problem
• A matrix Rodrigues formula for classical orthogonal polynomials in two variables
• Upward extension of the Jacobi matrix for orthogonal polynomials