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Research Article | Open Access

On certain properties of three parametric kinds of Apostol-type unified Bernoulli-Euler polynomials

William Ramírez1,4( ), Can Kızılateş2, Daniel Bedoya3, Clemente Cesarano4, Cheon Seoung Ryoo5
Department of Natural and Exact Sciences, Universidad de la Costa, Barranquilla 080002, Colombia
Department of Mathematics, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey
Departamento de Ciencias Básicas, Universidad Metropolitana, Barranquilla, Colombia
Section of Mathematics International Telematic University Uninettuno, Rome 00186, Italy
Department of Mathematics, Hannam University, Daejeon 34430, South Korea
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Abstract

In this paper, we define the three parametric types of Apostol-type unified Bernoulli-Euler polynomials. We present fundamental properties of these polynomials through the utilization of their generating functions. Furthermore, we derive the partial derivatives of these polynomials. Subsequently, we introduce bivariate polynomials and determine their zeros, graphical representations, and approximation values for specific parameters.

Keywords

unified Bernoulli-Euler polynomialsApostol-type polynomialspartial derivativesgenerating functions
CLC number: 11B68, 11B83, 11B39, 05A19

References

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 137-158
DOI: 10.3934/math.2025008

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Cite this article:
Ramírez W, Kızılateş C, Bedoya D, et al. On certain properties of three parametric kinds of Apostol-type unified Bernoulli-Euler polynomials. AIMS Mathematics, 2025, 10(1): 137-158. https://doi.org/10.3934/math.2025008

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Received: 28 September 2024
Revised: 02 December 2024
Accepted: 16 December 2024
Published: 15 January 2025
©2025 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)