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Asymptotics of Stirling and Chebyshev‐Stirling Numbers of the Second Kind
Author(s) -
Gawronski Wolfgang,
Littlejohn Lance L.,
Neuschel Thorsten
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12037
Subject(s) - stirling numbers of the first kind , stirling number , stirling numbers of the second kind , mathematics , stirling engine , bell polynomials , chebyshev filter , limit (mathematics) , asymptotic formula , chebyshev polynomials , pure mathematics , mathematical analysis , physics , thermodynamics
For the classical Stirling numbers of the second kind, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the Chebyshev–Stirling numbers, a special case of the Jacobi–Stirling numbers. Essential features are uniformity properties and the fact that the leading terms of the asymptotics are given explicitly and they contain elementary expressions only. Thereby supplements of the asymptotic analysis of these numbers are established.