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arXiv · 2308.01288

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

Amílcar Branquinho·Juan E. F. Díaz·Ana Foulquié-Moreno·Manuel Mañas
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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 ${}_3F_2$ 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-Pi\~neiro, 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-Pi\~neiro, 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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Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno, Manuel Mañas. 2023-08-02. Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials. https://arxiv.org/abs/2308.01288

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