A Comprehensive Study of Generalized Bivariate q-Laguerre Polynomials: Structural Properties and Applications

Authors

  • Haitham Ali Qawaqneh Al-Zaytoonah University of Jordan (ZUJ), Jordan.
  • Waseem Ahmad Khan Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O Box 1664, Al Khobar 31952, Saudi Arabia.
  • Hassen Aydi Institute Sup´erieur d’Informatique et des Techniques de Communication, Universit´e de Sousse, H. Sousse 4000, Tunisia.
  • Ugur Duran Department of Basic Sciences of Engineering, Iskenderun Technical University, Hatay 31200, Turkey.
  • Cheon Seoung Ryoo Department of Mathematics, Hannam University, Daejeon 34430, South Korea.

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6668

Keywords:

Quantum calculus, q-Laguerre polynomials, generalized 2V q-Laguerre polynomials, Quasi monomiality, Extension of monomiality priciple, q-Dilatation operator, Partial differential equations, Differential equations

Abstract

In this paper, utilizing zeroth-order q-Bessel Tricomi functions, we introduce the generalized bivariate q-Laguerre polynomials. Then, we establish the generalized bivariate q-Laguerre polynomials from the context of quasi-monomiality. We examine some of their properties, such as q-multiplicative operator property, q-derivative operator property, and two q-integro-differential equations. Additionally, we derive operational representations and three q-partial differential equations for the generalized bivariate q-Laguerre polynomials. Moreover, we draw the zeros of the new polynomials, forming 2D and 3D structures, and provide a table including approximate zeros of the generalized bivariate q-Laguerre polynomials.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Haitham Ali Qawaqneh, Waseem Ahmad Khan, Hassen Aydi, Ugur Duran, Cheon Seoung Ryoo

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How to Cite

A Comprehensive Study of Generalized Bivariate q-Laguerre Polynomials: Structural Properties and Applications. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6668. https://doi.org/10.29020/nybg.ejpam.v18i3.6668