  We introduce a new representation for the rescaled Appell polynomials and use
it to obtain asymptotic expansions to arbitrary order. This representation
consists of a finite sum and an integral over a universal contour (i.e.
independent of the particular polynomials considered within the Appell family).
We illustrate our method by studying the zero attractors for rescaled Appell
polynomials. We also discuss the asymptotics to arbitrary order of the rescaled
Bernoulli polynomials.

Classical Analysis and ODEs;Combinatorics