R_I biorthogonal polynomials of Hahn type

2022/09/15 by Luc Vinet, Vinet, Luc, Meri Zaimi +3
Materials Science · Mathematics · Physics and Astronomy · #33C45 #33C47 #47B36 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Optical Materials Research #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2209.07433

openalex publication_date 2022/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A finite family of R_I polynomials is introduced and studied. It consists in a set of polynomials of ₃F₂ form whose biorthogonality to an ensemble of rational functions is spelled out. These polynomials are shown to satisfy two generalized eigenvalue problems: in addition to their recurrence relation of R_I type, they are also found to obey a difference equation. Underscoring this bispectrality is a triplet of operators with tridiagonal actions.

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