Some numerical results on the behavior of zeros of the Hermite-Padé polynomials

2015/01/28 by Nikolay Ikonomov, N. R. Ikonomov, Ikonomov, N. R. +6 · 2 citations
Mathematics · Physics and Astronomy · #30E10 #41A21 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math.CV #msc:30E10 #msc:41A21

paper · pdf · doi:10.48550/arxiv.1501.07090

Bibliography: 71 titles; 79 pictures

arxiv created 2015/01/28 · openalex publication_date 2015/01/28 · arxiv updated 2015/01/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We introduce and analyze some numerical results obtained by the authors experimentally. These experiments are related to the well known problem about the distribution of the zeros of Hermite--Padé polynomials for a collection of three functions [f₀ ≡ 1,f₁,f₂]. The numerical results refer to two cases: a pair of functions f₁,f₂ forms an Angelesco system and a pair of functions f₁=f,f₂=f² forms a (generalized) Nikishin system. The authors hope that the obtained numerical results will set up a new conjectures about the limiting distribution of the zeros of Hermite--Padé polynomials.

Cited by

• Zero Distribution of Hermite-Padé Polynomials and Convergence Properties of Hermite Approximants for Multivalued Analytic Functions
• On the limit zero distribution of type I Hermite-Padé polynomials

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