eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2010-01-01
Vol. 12 no. 2
10.46298/dmtcs.501
501
journal article
Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach
Guy Louchard
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.
https://dmtcs.episciences.org/501/pdf
Stirling numbers
saddle point method
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]