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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotics of Stirling numbers of the second kind
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by W. E. Bleick and Peter C. C. Wang PDF
Proc. Amer. Math. Soc. 42 (1974), 575-580 Request permission

Erratum: Proc. Amer. Math. Soc. 48 (1975), 518.
Erratum: Proc. Amer. Math. Soc. 48 (1975), 518.

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
  • L. C. Hsu, Note on an asymptotic expansion of the $n$th difference of zero, Ann. Math. Statistics 19 (1948), 273–277. MR 24986, DOI 10.1214/aoms/1177730254
  • Leo Moser and Max Wyman, An asymptotic formula for the Bell numbers, Trans. Roy. Soc. Canada Sect. III 49 (1955), 49–54. MR 78489
  • N. G. de Bruijn, Asymptotic methods in analysis, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen; Interscience Publishers Inc., New York, 1958. MR 0099564
  • Leo Moser and Max Wyman, On solutions of $x^d=1$ in symmetric groups, Canadian J. Math. 7 (1955), 159–168. MR 68564, DOI 10.4153/CJM-1955-021-8
    • Konrad Knopp, Theory and applications of infinite series, Blackie and Son, London, 1928, pp. 523-528.
  • G. E. Roberts and H. Kaufman, Table of Laplace transforms, W. B. Saunders Co., Philadelphia-London, 1966. MR 0190638
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 575-580
  • MSC: Primary 41A60
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0330867-1
  • MathSciNet review: 0330867