Research Article

Representing polynomials by degenerate Bernoulli polynomials

Published in: Quaestiones Mathematicae
Volume 46 , issue 5 , 2023 , pages: 959–980

DOI: 10.2989/16073606.2022.2049912

Author(s): Dae San Kim Sogang University, Republic of Korea , Taekyun Kim Kwangwoon University, Republic of Korea

Keywords: 05A19 , 05A40 , 11B68 , 11B83 , Degenerate Bernoulli polynomial , higher-order degenerate Bernoulli polynomial , umbral calculus

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Abstract

In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples.

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