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Applicable Analysis and Discrete Mathematics
Article . 2013 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Asymptotics of the Stirling numbers of the second kind revisited

Authors: Louchard, Guy;

Asymptotics of the Stirling numbers of the second kind revisited

Abstract

Using the Saddle point method and multiseries expansions, we obtain from the generating function of the Stirling numbers of the second kind {n / m} and Cauchy's integral formula, asymptotic results in central and non-central regions. In the central region, we revisit the celebrated Gaussian theorem with more precision. In the region m = n - na, 1 > a > 1/2, we analyze the dependence of {n / m} on a. An extension of some Moser and Wyman's result to full m range is also provided. This paper fits within the framework of Analytic Combinatorics.

Related Organizations
Keywords

Multiseries expansions, Mathématiques, Saddle point method, Analyse mathématique, Asymptotics, Analytic combinatorics, Stirling numbers of the second kind

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Top 10%
Average
Average
gold