On discrete Appell polynomials of Apostol-Bernoulli-type polynomials and their patterns of distribution of zeros

Volume 39, Issue 2, pp 280--291 https://dx.doi.org/10.22436/jmcs.039.02.07

Publication Date: March 29, 2025 Submission Date: October 20, 2024 Revision Date: January 23, 2025 Accteptance Date: February 14, 2025

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Authors

M.-F. Heredia-Moyano - International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy. J. Hernandez - Escuela de Matematicas, Facultad de Ciencias, Universidad Autonoma de Santo Domingo, Dominican Republic. W. A. Khan - Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia. W. Ramirez - International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy. - Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Calle 58\(#\)55-66, Barranquilla, Colombia. Sh. A. Wani - Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed) University, Pune, India.

Abstract

This study introduces a new category of discrete Appell polynomials derived from Apostol-Bernoulli-type polynomials. We derive their generating function, provide explicit formulae, and represent them in matrix form to enhance computational efficiency and explore deeper algebraic properties. Using algebraic structure and recurrence relations to emphasize these recurrences, we develop the principle of monomiality for these polynomials. The study also approximates the roots of Apostol-Bernoulli-type discrete polynomials using numerical methods, underscoring their relevance in various applications. The paper concludes by discussing potential extensions and the broader impact of this work in combinatorial mathematics and numerical analysis.

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Keywords

• Discrete polynomials
• Apostol-Bernoulli-type polynomials
• distribution of zeros

MSC

•  33E20
•  33B10
•  45J05
•  65Q30
•  65R20

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