Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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
  • [4] Leo Moser and Max Wyman, On solutions of 𝑥^{𝑑}=1 in symmetric groups, Canad. J. Math. 7 (1955), 159–168. MR 0068564
  • [5] Konrad Knopp, Theory and applications of infinite series, Blackie and Son, London, 1928, pp. 523-528.
  • [6] G. E. Roberts and H. Kaufman, Table of Laplace transforms, W. B. Saunders Co., Philadelphia-London, 1966. MR 0190638

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A60

Retrieve articles in all journals with MSC: 41A60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0330867-1
Keywords: Asymptotic expansion, Stirling number of the second kind, Bell number, saddle point method
Article copyright: © Copyright 1974 American Mathematical Society