Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials

This study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-partial differential equations and investigate numerical aspects associated with these polynomials. Furthermore, we deduce the monomiality principle and other key properties of the bivariate 2D...

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Bibliographic Details
Published in:Open Mathematics
Main Authors: Wani Shahid Ahmad, Zayed Mohra, Nahid Tabinda
Format: Article
Language:English
Published: De Gruyter 2024-11-01
Subjects:
q-special polynomials
q-calculus
monomiality principle
explicit form
numerical representation
33e20
33c45
33b10
33e30
11t23
Online Access:https://doi.org/10.1515/math-2024-0080
Description
Summary:This study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-partial differential equations and investigate numerical aspects associated with these polynomials. Furthermore, we deduce the monomiality principle and other key properties of the bivariate 2D-qq Hermite polynomials, including qq-recurrence relations and qq-difference equations. In addition, the graphical representations for the bivariate 2D-qq Hermite polynomials and qq-Hermite polynomials are explored for different values of indices.
ISSN:2391-5455

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