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

Chunyan Li; Zhizheng Zhang; Chunyan Li; Zhizheng Zhang

doi:10.3934/math.2026845

AIMS Mathematics

2026, Volume 11, Issue 7: 20802-20814. doi: 10.3934/math.2026845

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Research article

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

Received: 20 April 2026 Revised: 22 June 2026 Accepted: 07 July 2026 Published: 14 July 2026
MSC : 11B68, 11B83

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.
- apostol Bernoulli-Lucas polynomials,
- apostol Euler-Lucas polynomials,
- Lucas sequence
Citation: Chunyan Li, Zhizheng Zhang. Apostol Bernoulli-Lucas polynomials, Apostol Euler-Lucas polynomials and their properties[J]. AIMS Mathematics, 2026, 11(7): 20802-20814. doi: 10.3934/math.2026845

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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.

References

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