Asymptotics of Stirling numbers of the second kind
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- by W. E. Bleick and Peter C. C. Wang
- Proc. Amer. Math. Soc. 42 (1974), 575-580
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330867-1
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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
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- Leo Moser and Max Wyman, An asymptotic formula for the Bell numbers, Trans. Roy. Soc. Canada Sect. III 49 (1955), 49β54. 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), 159β168. 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
Bibliographic 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