An Analytical Study of Two-Dimensional Bell Polynomials and Their Properties

Authors

  • Shahid Ahmad Wani Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India
  • Taghreed Alqurashi Mathematics Department, Faculty of Science, Al-Baha University, 65779-7738 Albaha City, Kingdom of Saudi, Arabia
  • William Ramírez Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58 N 55-66, 080002 Barranquilla, Colombia
  • Shilpa Malge Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India
  • Jesus David Berrio Valbuena Universidad del Atl´antico, Barranquilla, Colombia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6054

Keywords:

2D Special Polynomials, Generating function, Series representation

Abstract

This study investigates two-dimensional Bell polynomials, emphasizing their fundamental properties and applications in mathematical analysis. Utilizing the framework of generating functions, we derive explicit representations, summation formulae, recurrence relations, and addition formulas for these polynomials. Additionally, we present their matrix form and product formula, further enriching their structural analysis. Furthermore, we introduce the 2D Bell-based Stirling polynomials of the second kind and explore their associated properties. This research aims to enhance the theoretical understanding of Bell polynomials and their broader applications in mathematical analysis.  

Author Biography

  • William Ramírez, Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58 N 55-66, 080002 Barranquilla, Colombia

    Section of Mathematics International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186
    Rome, Italy

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Complex Analysis

License

Copyright (c) 2025 Shahid Ahmad Wani, Taghreed Alqurashi, William Ramírez, Shilpa Malge, Jesus David Berrio Valbuena

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How to Cite

An Analytical Study of Two-Dimensional Bell Polynomials and Their Properties. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6054. https://doi.org/10.29020/nybg.ejpam.v18i3.6054