Explicit upper bounds for Touchard polynomials and Bell numbers

期刊论文
发表日期：

2024年1月31日

查看全文

A.-M. Acu,
J. A. Adell,
I. Raşa

摘要

We obtain explicit upper bounds for the Touchard polynomials $T_n(x)$ $T_{n} (x)$ , for $x>0$ $x > 0$ . When applied to the Bell numbers $B_n=T_n(1)$ $B_{n} = T_{n} (1)$ , such boundsare asymptotically sharp. A simple probabilistic approach based on estimatesof moments of nonnegative random variables is used. Applications giving upperbounds for the moments of a certain subset of Jakimovski-Leviatan operators arealso provided.