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Liviu I. Nicolaescu
Derangements and asymptotics of the Laplace transforms of large powers of a polynomial
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| Published: |
April 12, 2004 |
| Keywords: |
derangements, Laplace transforms, asymptotics, multinomial distributions |
| Subject: |
44A10, 05A05, 05A10, 05A16, 41A60, 33C45 |
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Abstract
We use a probabilistic approach to produce sharp asymptotic estimates as
n→∞ for the Laplace transform of Pn, where P is a
fixed complex polynomial. As a consequence we obtain a new
elementary proof of a result of Askey-Gillis-Ismail-Offer-Rashed
in the combinatorial theory of derangements.
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| Acknowledgements
This work was partially suported by the NSF grant DMS-0303601.
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| Author information
Dept. of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618
nicolaescu.1@nd.edu
http://www.nd.edu/~lnicolae/
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