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Asymptotics of Stirling numbers of the second kind

Authors: W. E. Bleick and Peter C. C. Wang
Journal: Proc. Amer. Math. Soc. 42 (1974), 575-580
MSC: Primary 41A60
Erratum: Proc. Amer. Math. Soc. 48 (1975), 518.
Erratum: Proc. Amer. Math. Soc. 48 (1975), 518.
MathSciNet review: 0330867
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Abstract: A complete asymptotic development of the Stirling numbers $ S(N,K)$ of the second kind is obtained by the saddle point method previously employed by Moser and Wyman [Trans, Roy. Soc. Canad., 49 (1955), 49-54] and de Bruijn [Asymptotic methods in analysis, North-Holland, Amsterdam, 1958, pp. 102-109] for the asymptotic representation of the related Bell numbers.

References [Enhancements On Off] (What's this?)

  • [1] L. C. Hsu, Note on an asymptotic expansion of the 𝑛th difference of zero, Ann. Math. Statistics 19 (1948), 273–277. MR 0024986
  • [2] Leo Moser and Max Wyman, An asymptotic formula for the Bell numbers, Trans. Roy. Soc. Canada. Sect. III. (3) 49 (1955), 49–54. MR 0078489
  • [3] N. G. de Bruijn, Asymptotic methods in analysis, Bibliotheca Mathematica. Vol. 4, North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen; Interscience Publishers Inc., New York, 1958. MR 0099564
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Keywords: Asymptotic expansion, Stirling number of the second kind, Bell number, saddle point method
Article copyright: © Copyright 1974 American Mathematical Society