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arXiv · 2609.07678

Pi\~neiro mixed orthogonal polynomials and bidiagonal factorization

Amílcar Branquinho·Juan E. F. Díaz·Ana Foulquié-Moreno·Manuel Mañas
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Abstract

We study mixed multiple orthogonal polynomials associated with rank-one matrices of measures and their recurrence relations. On the step line we identify the corresponding banded recurrence matrix through the Gauss--Borel factorization of the moment matrix. Elementary Christoffel transformations lead to a factorization of this recurrence matrix into lower and upper bidiagonal factors. For the mixed Pi\~neiro system we derive contour-integral and generalized hypergeometric representations and formulas for the recurrence and factorization coefficients.

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Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno, Manuel Mañas. 2026-09-07. Pi\~neiro mixed orthogonal polynomials and bidiagonal factorization. https://arxiv.org/abs/2609.07678

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