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

Farid Bencherif; Rachid Boumahdi; Tarek Garici

Communications in Mathematics (2021)

  • Volume: 29, Issue: 3, page 343-355
  • ISSN: 1804-1388

Abstract

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Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x ) with A 0 ( x ) a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.

How to cite

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Bencherif, Farid, Boumahdi, Rachid, and Garici, Tarek. "Symmetric identity for polynomial sequences satisfying $A_{n+1}^\prime (x)=(n+1)A_n(x)$." Communications in Mathematics 29.3 (2021): 343-355. <http://eudml.org/doc/297504>.

@article{Bencherif2021,
abstract = {Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying $A_\{n+1\}^\prime (x) =(n+1)A_\{n\}(x)$ with $A_0(x)$ a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.},
author = {Bencherif, Farid, Boumahdi, Rachid, Garici, Tarek},
journal = {Communications in Mathematics},
keywords = {Appell sequence; Apostol-Bernoulli polynomial; Apostol-Euler polynomial; generalized Bernoulli polynomial; primitive Dirichlet character},
language = {eng},
number = {3},
pages = {343-355},
publisher = {University of Ostrava},
title = {Symmetric identity for polynomial sequences satisfying $A_\{n+1\}^\prime (x)=(n+1)A_n(x)$},
url = {http://eudml.org/doc/297504},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Bencherif, Farid
AU - Boumahdi, Rachid
AU - Garici, Tarek
TI - Symmetric identity for polynomial sequences satisfying $A_{n+1}^\prime (x)=(n+1)A_n(x)$
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 3
SP - 343
EP - 355
AB - Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying $A_{n+1}^\prime (x) =(n+1)A_{n}(x)$ with $A_0(x)$ a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.
LA - eng
KW - Appell sequence; Apostol-Bernoulli polynomial; Apostol-Euler polynomial; generalized Bernoulli polynomial; primitive Dirichlet character
UR - http://eudml.org/doc/297504
ER -

References

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