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arXiv · 2404.13958

Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation

Amílcar Branquinho·Juan EF Díaz·Ana Foulquié-Moreno·Manuel Mañas
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Abstract

This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Pi\~neiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials.

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Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, Manuel Mañas. 2024-04-22. Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation. https://arxiv.org/abs/2404.13958

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