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

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 F23 and is proven using recently discovered contiguous relations. Moreov...

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Bibliographic Details
Published in:Linear algebra and its applications 2024-03
Main Authors: Branquinho, Amílcar, Díaz, Juan E.F., Foulquié-Moreno, Ana, Mañas, Manuel
Format: Article
Language:English
Subjects:
AT systems
Hahn
Hessenberg matrices
Hypergeometric series
Jacobi–Piñeiro
Laguerre
Meixner
Multiple orthogonal polynomials
Recursion matrix
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Summary: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 F23 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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2024.03.033