2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69921We use a probabilistic approach to describe the behavior as $n -> \infty$ of the Laplace transforms of $P^n$, where $P$ a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer in the combinatorial theory of derangements.15 pages, LaTeXClassical Analysis and ODEsCombinatorics41A10,44A10, 05A10,05A16text