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Published: 
April 12, 2004

Keywords: 
derangements, Laplace transforms, asymptotics, multinomial distributions

Subject: 
44A10, 05A05, 05A10, 05A16, 41A60, 33C45

Abstract:

We use a probabilistic approach to produce sharp asymptotic estimates as
$n\ra \infty$ for the Laplace transform of $P^n$, where $P$ is a
fixed complex polynomial. As a consequence we obtain a new
elementary proof of a result of AskeyGillisIsmailOfferRashed, [1, 3]
in the combinatorial theory of derangements.

Acknowledgments:
This work was partially suported by the NSF grant DMS0303601.
Author information:
Dept. of Mathematics, University of Notre Dame, Notre Dame, IN 465564618
nicolaescu.1@nd.edu
http://www.nd.edu/~lnicolae/
 