Investigating 2-iterated degenerate 2D Appell polynomials and their diverse applications

Volume 38, Issue 4, pp 521--534 https://dx.doi.org/10.22436/jmcs.038.04.07

Publication Date: February 14, 2025 Submission Date: March 29, 2024 Revision Date: August 29, 2024 Accteptance Date: January 10, 2025

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Authors

S. A. Wani - Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed) University, Pune, India. C. Lande - Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed) University, Pune, India. F. A. F. Gandara - Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58 No. 55-66, 080002 Barranquilla, Colombia. W. A. Khan - Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia.

Abstract

This research delves into the realm of special polynomials, emphasizing the integration of the monomiality principle alongside operational rules and related properties. Through a comprehensive investigation, a novel category of polynomials termed the 2-iterated degenerate 2D Appell polynomials is introduced, leveraging the monomiality principle. The study uncovers fresh insights that align with previous research endeavors and presents explicit formulas and crucial properties of these polynomials. Furthermore, connections are established between the 2-iterated degenerate 2D Appell polynomials and other polynomial families such as the Bernoulli, Euler, and Genocchi polynomials. Leveraging these interconnections, additional results are derived. By recognizing the aforementioned polynomials as initial members of the Appell family and employing the principle of monomiality, this investigation significantly contributes to the expansion of knowledge in the domain of special polynomials.

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Keywords

• Two-iterated degenerate 2D Appell polynomials
• monomiality principle
• explicit forms
• determinant form

MSC

•  33E20
•  33B10
•  33E30
•  11T23

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