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arXiv · 1501.07090

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

N. R. Ikonomov·R. K. Kovacheva·S. P. Suetin
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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 $[f_0 \equiv 1,f_1,f_2]$. The numerical results refer to two cases: a pair of functions $f_1,f_2$ forms an Angelesco system and a pair of functions $f_1=f,f_2=f^2$ 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.

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N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin. 2015-01-28. Some numerical results on the behavior of zeros of the Hermite-Padé polynomials. https://arxiv.org/abs/1501.07090

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