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Research Article | Open Access

Apostol Bernoulli-Lucas polynomials, Apostol Euler-Lucas polynomials and their properties

Chunyan Li( ), Zhizheng Zhang
School of Mathematics and Statistics, Xinxiang University, Xinxiang, Henan 453003, China
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Abstract

Two new famlies of polynomials were defined, namely, Apostol Bernoulli-Lucas polynomials and Apostol Euler-Lucas polynomials. The properties of these two polynomials were investigated, including explicit relations, diffference equations, summation formulae, and differential recurrence relations.

Keywords

apostol Bernoulli-Lucas polynomialsapostol Euler-Lucas polynomialsLucas sequence
CLC number: 11B68, 11B83

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AIMS Mathematics
Volume 11 Issue 7,
July 2026
Pages 20802-20814
DOI: 10.3934/math.2026845

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Cite this article:
Li C, Zhang Z. Apostol Bernoulli-Lucas polynomials, Apostol Euler-Lucas polynomials and their properties. AIMS Mathematics, 2026, 11(7): 20802-20814. https://doi.org/10.3934/math.2026845

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Received: 20 April 2026
Revised: 22 June 2026
Accepted: 07 July 2026
Published: 15 July 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)