par Louchard, Guy
Référence Applicable Analysis and Discrete Mathematics, 7, 2, page (193-210)
Publication Publié, 2013
Article révisé par les pairs
Résumé : 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 - nα, 1 > α > 1/2, we analyze the dependence of {n m} on α. 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.