Appell和Sheffer序列：通过泛函和例子对其进行刻画
Appell and Sheffer sequences: on their characterizations through functionals and examples
摘要：
本文的目的是提出一个新的简单的递归Appell和Sheffer序列的线性泛函，定义它们，并解释这是如何相当于几个著名的特征出现在文献中。我们还给出了几个例子，包括与伯努利和欧拉多项式相关的逆算子的整表示，和一个新的整表示的重新缩放的埃尔米特$d$ -正交多项式推广的维尔斯特拉斯算子有关的埃尔米特多项式。
英文摘要：
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 $d$-orthogonal polynomials generalizing the Weierstrass operator related to the Hermite polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
