Noncommutative Biorthogonal Polynomials

2010/09/28 by Emily Sergel, Sergel, Emily
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math-ph #math.MP #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.1009.5472

12 pages, 0 figures

openalex publication_date 2010/09/28 · arxiv created 2011/05/01 · arxiv updated 2011/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The idea of orthogonal polynomials has been generalized in two ways to achieve new types of polynomials: noncommutative orthogonal polynomials and biorthogonal polynomials. This paper brings these two different generalizations together to present a completely algebraic definition of noncommutative biorthogonal polynomials. It then goes on to obtain recurrence relations for some types of biorthogonal polynomials and concludes with a broad extension of Favard's theorem.

Related

• Finite biorthogonal polynomials suggested by the finite orthogonal polynomials M_n^(p,q)(x)
• A hypergeometric sequence of biorthogonal polynomials and its relationship with Meixner-Pollaczek polynomials
• Laurent Biorthogonal Polynomials and Riordan Arrays
• Relations on noncommutative variables and associated orthogonal polynomials
• Finite bivariate biorthogonal N-Konhauser polynomials