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Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach

Abstract : Using the saddle point method, we obtain from the generating function of the Stirling numbers of the first kind [n j] and Cauchy's integral formula, asymptotic results in central and non-central regions. In the central region, we revisit the celebrated Goncharov theorem with more precision. In the region j = n - n(alpha); alpha > 1/2, we analyze the dependence of [n j] on alpha.
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Guy Louchard. Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (2), pp.167-184. ⟨hal-00990462⟩

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