Appell and Sheffer sequences: on their characterizations through functionals and examples
Classical Analysis and ODEs
2021-03-24 v1
Abstract
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the literature. We also give several examples, including integral representations of the inverse operators associated to Bernoulli and Euler polynomials, and a new integral representation of the re-scaled Hermite -orthogonal polynomials generalizing the Weierstrass operator related to the Hermite polynomials.
Cite
@article{arxiv.2010.09702,
title = {Appell and Sheffer sequences: on their characterizations through functionals and examples},
author = {Sergio A. Carrillo and Miguel Hurtado},
journal= {arXiv preprint arXiv:2010.09702},
year = {2021}
}