Louchard, Guy - Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach

dmtcs:501 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 2
Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach

Authors: Louchard, Guy

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.


Source : oai:HAL:hal-00990462v1
Volume: Vol. 12 no. 2
Published on: January 1, 2010
Submitted on: March 26, 2015
Keywords: Stirling numbers,saddle point method,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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