Certain Properties of $\Delta_h$ Legendre Polynomials and Applications in Computer Modelling

Authors

  • Shahid Ahmad Wani Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, Maharashtra, India
  • Waseem Ahmad Khan Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O Box 1664, Al Khobar 31952, Saudi Arabia
  • Taghreed Alqurashi Mathematics Department, Faculty of Science, Al-Baha University, 65779-7738, Albaha city, Kingdom of Saudi
  • Javid Gani Dar Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, Maharashtra, India
  • Dxion Salcedo Computer Science and Electronics Development, Universidad de la Costa, Barranquilla, Colombia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5886

Keywords:

$\Delta_h$ sequences, Monomiality principle, explicit forms, Determinant form, Symmetric identities

Abstract

This study investigates the development of polynomials, with a particular focus on the unique \(\Delta_h\) Legendre polynomials. Explicit formulas for these polynomials are derived, along with summation formulae that provide further structural insights. Additionally, the monomiality principle is established, reinforcing the algebraic framework of these polynomials. Symmetric identities are also formulated, highlighting their fundamental properties. The study concludes with remarks summarizing the key findings and potential directions for future research.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Physics

License

Copyright (c) 2025 Shahid Ahmad Wani, Waseem Ahmad Khan, Taghreed Alqurashi, Javid Gani Dar, Dxion Salcedo

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How to Cite

Certain Properties of $\Delta_h$ Legendre Polynomials and Applications in Computer Modelling. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5886. https://doi.org/10.29020/nybg.ejpam.v18i2.5886