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arXiv · 2602.15718

Asymptotics and zero behaviour of geometric polynomials

M. Bello-Hernández·M. Benito·Ó. Ciaurri·E. Fernández
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Abstract

We obtain some results on the asymptotic behaviour of Geometric polynomials in both the complex plane minus $[-1,0]$ and the interval $(-1,0)$. We also find the distance of consecutive zeros of these polynomials in the bulk of the interval $(-1,0)$. We also prove that they satisfy certain orthogonality properties. Due to their relationship with Eulerian polynomials, the results for Geometric polynomials can be transferred to Eulerian polynomials verbatim.

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M. Bello-Hernández, M. Benito, Ó. Ciaurri, E. Fernández. 2026-02-17. Asymptotics and zero behaviour of geometric polynomials. https://arxiv.org/abs/2602.15718

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