Asymptotics and zero behaviour of geometric polynomials
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arXiv
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| Format: | Preprint |
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2026
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| author | Bello-Hernández, M. Benito, M. Ciaurri, Ó. Fernández, E. |
| author_facet | Bello-Hernández, M. Benito, M. Ciaurri, Ó. Fernández, E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15718 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics and zero behaviour of geometric polynomials Bello-Hernández, M. Benito, M. Ciaurri, Ó. Fernández, E. Classical Analysis and ODEs Combinatorics Number Theory 11B83, 33C47, 41A46 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. |
| title | Asymptotics and zero behaviour of geometric polynomials |
| topic | Classical Analysis and ODEs Combinatorics Number Theory 11B83, 33C47, 41A46 |
| url | https://arxiv.org/abs/2602.15718 |