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

William Ramírez; Can Kızılateş; Daniel Bedoya; Clemente Cesarano; Cheon Seoung Ryoo; William Ramírez; Can Kızılateş; Daniel Bedoya; Clemente Cesarano; Cheon Seoung Ryoo

doi:10.3934/math.2025008

AIMS Mathematics

2025, Volume 10, Issue 1: 137-158. doi: 10.3934/math.2025008

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

1.
Department of Natural and Exact Sciences, Universidad de la Costa, Barranquilla 080002, Colombia
2.
Department of Mathematics, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey
3.
Departamento de Ciencias Básicas, Universidad Metropolitana, Barranquilla, Colombia
4.
Section of Mathematics International Telematic University Uninettuno, Rome 00186, Italy
5.
Department of Mathematics, Hannam University, Daejeon 34430, South Korea

Received: 28 September 2024 Revised: 02 December 2024 Accepted: 16 December 2024 Published: 02 January 2025
MSC : 11B68, 11B83, 11B39, 05A19

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.
- unified Bernoulli-Euler polynomials,
- Apostol-type polynomials,
- partial derivatives,
- generating functions
Citation: William Ramírez, Can Kızılateş, Daniel Bedoya, Clemente Cesarano, Cheon Seoung Ryoo. On certain properties of three parametric kinds of Apostol-type unified Bernoulli-Euler polynomials[J]. AIMS Mathematics, 2025, 10(1): 137-158. doi: 10.3934/math.2025008

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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.

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