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Symmetric identity for polynomial sequences satisfying A′n+1(x) = (n + 1)An(x)

Symmetric identity for polynomial sequences satisfying A′n+1(x) = (n + 1)An(x) AbstractUsing umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A′n+1(x) = (n + 1)An(x) with A0(x) a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, Apostol--Euler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

Symmetric identity for polynomial sequences satisfying A′n+1(x) = (n + 1)An(x)

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Publisher
de Gruyter
Copyright
© 2021 Farid Bencherif et al., published by Sciendo
eISSN
2336-1298
DOI
10.2478/cm-2021-0011
Publisher site
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Abstract

AbstractUsing umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A′n+1(x) = (n + 1)An(x) with A0(x) a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, Apostol--Euler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.

Journal

Communications in Mathematics – de Gruyter

Published: Dec 1, 2021

Keywords: Appell sequence; Apostol-Bernoulli polynomial; Apostol-Euler polynomial; generalized Bernoulli polynomial; primitive Dirichlet character; 05A19; 05A40; 11B68

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