A noncommutative identity for the Appell polynomials
type: Item
instance of: scholarly article
title: A noncommutative identity for the Appell polynomials
zbMATH Open document ID: 0931.33013
DOI: 10.1007/BF02310314
author: O. V. Viskov
published in: Mathematical Notes
publication date: 2000-03-02T00:00:00Z
review text: A sequence of Appell polynomials is defined as a sequence \(A=\{a_n(x),n\geq 0\}\) of polynomials \(a_n(x)\) satisfying the properties: (a) have the degree equal to \(n\); (b) behave like power-law functions under differentiation, i.e. \({da_n(x) \over dx}= na_{-1}(x)\), \(n=0,1, \dots\). It is shown that the Appell polynomials satisfy a simple identity which forms the basis of many analytic results that appear, at first glance, to be disconnected. In particular, the author uniformly derives Taylor's expansion with remainder in Cauchy's form, the universal Bernoulli series, and the Euler-MacLaurin summation formula.
Mathematics Subject Classification ID: 33C65
zbMATH DE Number: 1274244
zbMATH Keywords: Bernoulli polynomial
zbMATH Keywords: Taylor expansion
zbMATH Keywords: Appell polynomials
zbMATH Keywords: Euler-MacLaurin summation formula
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: Q5725805
cites work: A Property of Appell Sets
cites work: Q5519244
cites work: Q3886969
cites work: Probability measures, Appell polynomials and polynomial approximation
description: scientific article; zbMATH DE number 1274244