# On the asymptotics of the rescaled Appell polynomials

## TL;DR

This paper introduces a new universal integral representation for rescaled Appell polynomials, enabling detailed asymptotic analysis and zero attractor studies, with applications to Bernoulli polynomials.

## Contribution

It provides a novel, universal integral representation for rescaled Appell polynomials and develops asymptotic expansions of arbitrary order.

## Key findings

- Derived asymptotic expansions for rescaled Appell polynomials
- Analyzed zero attractors for these polynomials
- Discussed asymptotics of rescaled Bernoulli 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.