Contents

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Asymptotics of the Eulerian numbers revisited: A large deviation analysis

Guy Louchard1
1UNIVERSITÉ LIBRE DE BRUXELLES, BELGIUM, DÉPARTEMENT D’INFORMATIQUE, CP 212, BOULEVARD DU TRIOMPHE, B-1050 BRUXELLES, BELGIUM

Abstract

Using the Saddle point method and multiseries expansions, we obtain from the generating function of the Eulerian numbers An,k and Cauchy’s integral formula, asymptotic results in non-central region. In the region k=nnα, 1>α>1/2, we analyze the dependence of An,k on α. This paper fits within the framework of Analytic Combinatorics.

Keywords: Eulerian numbers, Asymptotics, Saddle point method, Multiseries expansions, Analytic Combinatorics.