Appell and Sheffer sequences: on their characterizations through functionals and examples

DOI10.5802/crmath.172zbMath1459.05022arXiv2010.09702OpenAlexW3136247010MaRDI QIDQ2658218

Sergio A. Carrillo, Miguel Hurtado

Publication date: 19 March 2021

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.09702

zbMATH Keywords

BernoulliEuler and Hermite \(d\)-orthogonal polynomialsSheffer and Appell sequences

Mathematics Subject Classification ID

Umbral calculus (05A40) Bernoulli and Euler numbers and polynomials (11B68) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Special sequences and polynomials (11B83)

Related Items (1)

A method for summing Bessel series and a couple of illustrative examples

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A matrix approach to Sheffer polynomials
• Probabilistic approach to Appell polynomials
• A determinantal approach to Sheffer sequences
• A determinantal approach to Appell polynomials
• Operational formulas connected with two generalizations of Hermite polynomials
• The umbral calculus
• Appell polynomials as values of special functions
• The relation of the \(d\)-orthogonal polynomials to the Appell polynomials
• Formal power series and linear systems of meromorphic ordinary differential equations
• Ramanujan summation of divergent series
• Closed form expressions for Appell polynomials
• Characterization of Kummer hypergeometric Bernoulli polynomials and applications
• Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials
• Binomial convolution and transformations of Appell polynomials
• On Appell sequences of polynomials of Bernoulli and Euler type
• Sur les cycles des substitutions
• On the Lerch zeta function
• Euler-Boole Summation Revisited
• Functions de variable réelle
• Determinant representations of Appell polynomial sequences
• Existence and reduction of generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
• A unified matrix approach to the representation of Appell polynomials
• An algebraic approach to Sheffer polynomial sequences
• HYPERGEOMETRIC BERNOULLI POLYNOMIALS AND APPELL SEQUENCES
• The Stieltjes moment problem for functions of bounded variation
• Note on Appell polynomials
• A Property of Appell Sets

This page was built for publication: Appell and Sheffer sequences: on their characterizations through functionals and examples