Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-00990462
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Tuesday, May 13, 2014 - 3:37:43 PM
Last modification on : Tuesday, October 19, 2021 - 12:55:35 PM
Long-term archiving on: : Monday, April 10, 2017 - 10:16:16 PM

File

1308-5002-1-PB.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Guy Louchard. Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, Vol. 12 no. 2 (2), pp.167-184. ⟨10.46298/dmtcs.501⟩. ⟨hal-00990462⟩

Share

Metrics

Record views

39

Files downloads

632