On the asymptotics of the rescaled Appell polynomials

Abstract: 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.