Explicit upper bounds for Touchard polynomials and Bell numbers

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-01-31 DOI:10.1007/s10474-024-01401-6

A.-M. Acu, J. A. Adell, I. Raşa

引用次数: 0

Abstract

We obtain explicit upper bounds for the Touchard polynomials \(T_n(x)\), for \(x>0\). When applied to the Bell numbers \(B_n=T_n(1)\), such bounds are asymptotically sharp. A simple probabilistic approach based on estimates of moments of nonnegative random variables is used. Applications giving upper bounds for the moments of a certain subset of Jakimovski-Leviatan operators are also provided.

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Touchard多项式和贝尔数的显式上限

对于 \(x>0\), 我们得到了Touchard多项式（T_n(x)\）的明确上限。当应用到贝尔数 \(B_n=T_n(1)\) 时，这种边界是渐近尖锐的。使用了一种基于非负随机变量矩估计的简单概率方法。还提供了给出 Jakimovski-Leviatan 算子的某个子集的矩的上限的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.