View paper:
pdf dvi ps
View abstract:
pdf gif
links page

Graphical interface
Volume 10
Other volumes
Full text search
of NYJM papers
NYJM home

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

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

Liviu I. Nicolaescu

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 $n\ra \infty$ 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 Askey-Gillis-Ismail-Offer-Rashed, [1, 3] 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