New York Journal of Mathematics
Volume 10 (2004) 117-131


Liviu I. Nicolaescu

Derangements and asymptotics of the Laplace transforms of large powers of a polynomial

Published: April 12, 2004
Keywords: derangements, Laplace transforms, asymptotics, multinomial distributions
Subject: 44A10, 05A05, 05A10, 05A16, 41A60, 33C45

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.


This work was partially suported by the NSF grant DMS-0303601.

Author information

Dept. of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618