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arXiv · 2502.19326

Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach

Amílcar Branquinho·Ana Foulquié-Moreno·Assil Fradi·Manuel Mañas
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Abstract

We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for the matrix orthogonal polynomials and functions of second kind. It is shown that the corresponding matrix recurrence coefficients satisfy a non-Abelian extensions of a family of discrete Painlev\'e d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type.

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Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi, Manuel Mañas. 2025-02-26. Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach. https://arxiv.org/abs/2502.19326

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