Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials

2023/08/02 by Amílcar Branquinho, Juan E. F. Díaz, Branquinho, Amílcar +5
Chemistry · Engineering · Physics and Astronomy · #33C45 #33C47 #42C05 #47B36 #47B39 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Optical Polarization and Ellipsometry #Optical and Acousto-Optic Technologies

paper · pdf · doi:10.48550/arxiv.2308.01288

openalex publication_date 2023/08/02 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/29

Abstract

This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios involving the generalized hypergeometric function ₃F₂ and is proven using recently discovered contiguous relations. Moreover, employing the multiple Askey scheme, a bidiagonal factorization is derived for the Hahn descendants, including Jacobi-Piñeiro, multiple Meixner (kinds I and II), multiple Laguerre (kinds I and II), multiple Kravchuk, and multiple Charlier, all represented in terms of hypergeometric functions. For the cases of multiple Hahn, Jacobi-Piñeiro, Meixner of kind II, and Laguerre of kind I, where there exists a region where the recurrence matrix is nonnegative, subregions are identified where the bidiagonal factorization becomes a positive bidiagonal factorization.

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• Hahn multiple orthogonal polynomials of type I: Hypergeometrical expressions
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• Classical discrete multiple orthogonal polynomials: hypergeometric and integral representations