On an extension of generalized coherent pairs of orthogonal polynomials: the classical case

2023/02/24 by Jong Hwan Lee, Lee, Jong Hwan, Sung Jun An +3
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2302.13811

openalex publication_date 2023/02/24 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28

Abstract

Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended coherent pairs and extended symmetric coherent pairs and find the related coefficients. When one of the moment functionals is (strongly) classical, we find another orthogonal polynomial system to find three-term recurrence coefficients. Moreover, we determine the companion moment functional as a rational modification of the classical one.

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