Elementary asymptotics for the Stirling numbers of the second kind: The central range
math.CO2026-05v1license
Abstract
We derive the local and central limit theorems for the Stirling numbers of the second kind by elementary means, obtaining as corollaries effective asymptotic estimates for the Bell numbers and for the moments of the distribution. We also develop asymptotic expansions along several directions, all based on a novel finite-differencing approach; this provides the first self-contained elementary justification of such expansions.
Comments: 46 pages, 17 figures
Cite
@article{arxiv.2605.29633,
title = {Elementary asymptotics for the Stirling numbers of the second kind: The central range},
author = {Hsien-Kuei Hwang and Chong-Yi Li and Vytas Zacharovas},
journal= {arXiv preprint arXiv:2605.29633},
year = {2026}
}