On the asymptotic normality of the Legendre-Stirling numbers of thesecond kind

Gawronski, Wolfgang;Littlejohn, Lance L.;Neuschel, Thorsten
(2015) European Journal of Combinatorics — Vol. 49, p. 218-231 (2015)

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Authors
  • Gawronski, WolfgangUniversity of Trier
    Author
  • Littlejohn, Lance L.Baylor University
    Author
  • Neuschel, ThorstenUCLouvain
    Author
Abstract
For the Legendre–Stirling numbers of the second kind asymptotic formulae are derived in terms of a local central limit theorem. Thereby, supplements of the recently published asymptotic analysis of the Chebyshev–Stirling numbers are established. Moreover, we provide results on the asymptotic normality and unimodality for modified Legendre–Stirling numbers.
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Gawronski, W., Littlejohn, L. L., & Neuschel, T. (2015). On the asymptotic normality of the Legendre-Stirling numbers of thesecond kind. European Journal of Combinatorics, 49, 218-231. https://doi.org/10.1016/j.ejc.2015.03.014 (Original work published 2015)