Geodesic
Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach
Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2.

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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. 
@article{DMTCS_2010_12_2_a6,
     author = {Louchard, Guy},
     title = {Asymptotics of the {Stirling} numbers of the first kind revisited: {A} saddle point approach},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2010},
     doi = {10.46298/dmtcs.501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.501/}
}
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Louchard, Guy. Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach. Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2. doi : 10.46298/dmtcs.501. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.501/

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