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

Haitham Qawaqneh; Waseem Ahmad Khan; Hassen Aydi; Ugur Duran; Cheon Seoung Ryoo

doi:10.29020/nybg.ejpam.v18i3.6668

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

Haitham Qawaqneh^*, Waseem Ahmad Khan, Hassen Aydi, Ugur Duran, Cheon Seoung Ryoo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	6668
Journal	European Journal of Pure and Applied Mathematics
Volume	18
Issue number	3
DOIs	https://doi.org/10.29020/nybg.ejpam.v18i3.6668
Publication status	Published - Jul 2025
Externally published	Yes

Keywords

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

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10.29020/nybg.ejpam.v18i3.6668

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title = "A Comprehensive Study of Generalized Bivariate q-Laguerre Polynomials: Structural Properties and Applications",

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.",

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

author = "Haitham Qawaqneh and Khan, \{Waseem Ahmad\} and Hassen Aydi and Ugur Duran and Ryoo, \{Cheon Seoung\}",

note = "Publisher Copyright: {\textcopyright} 2025 The Author(s).",

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doi = "10.29020/nybg.ejpam.v18i3.6668",

language = "English",

volume = "18",

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T1 - A Comprehensive Study of Generalized Bivariate q-Laguerre Polynomials

T2 - Structural Properties and Applications

AU - Qawaqneh, Haitham

AU - Khan, Waseem Ahmad

AU - Aydi, Hassen

AU - Duran, Ugur

AU - Ryoo, Cheon Seoung

PY - 2025/7

Y1 - 2025/7

N2 - 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.

AB - 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.

KW - Differential equations

KW - Extension of monomiality priciple

KW - Partial differential equations

KW - Quantum calculus

KW - Quasi monomiality

KW - generalized 2V q-Laguerre polynomials

KW - q-Dilatation operator

KW - q-Laguerre polynomials

UR - https://www.scopus.com/pages/publications/105013820595

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DO - 10.29020/nybg.ejpam.v18i3.6668

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SN - 1307-5543

VL - 18

JO - European Journal of Pure and Applied Mathematics

JF - European Journal of Pure and Applied Mathematics

IS - 3

M1 - 6668

ER -

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

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