ASYMPTOTICS OF THE STIRLING NUMBERS OF THE SECOND KIND REVISITED

Applicable Analysis and Discrete Mathematics

article

Guy Louchard¹ 

[1] Universit´e Libre de Bruxelles

关键词: Stirling numbers of the second kind;    Asymptotics;    Saddle point method;    Multiseries expansions;    Analytic Combinatorics;   

DOI  :  10.2298/AADM130612011L

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Using the Saddle point method and multiseries expansions, we obtain fromthe generating function of the Stirling numbers of the second kind n nmoand Cauchy’s integral formula, asymptotic results in central and non-centralregions. In the central region, we revisit the celebrated Gaussian theoremwith more precision. In the region m = n − nα, 1 > α > 1/2, we analyzethe dependence of n nmoon α. An extension of some Moser and Wyman’sresult to full m range is also provided. This paper fits within the frameworkof Analytic Combinatorics.

【 授权许可】

Unknown