@article{Zayed2025, 
author = {Mohra Zayed and Taghreed Alqurashi and Shahid Ahmad Wani and Cheon Seoung Ryoo and William Ramírez},
title = {Several characterizations of bivariate quantum-Hermite-Appell Polynomials and the structure of their zeros},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {11184-11207},
keywords = {special functions, quantum calculus, explicit form, operational connection, structure of zeros, determinant form},
url = {https://www.sciopen.com/article/10.3934/math.2025507},
doi = {10.3934/math.2025507},
abstract = {This paper investigated the fundamental characteristics and uses of a new class of bivariate quantum-Hermite-Appell polynomials. The series representation and generating relation for these polynomials were derived. Also, a determinant representation for these polynomials was derived. Further, important mathematical characteristics were derived, such as    q-recurrence relations and    q-difference equations. These polynomials' numerical features were methodically examined, providing information on their computational possibilities and the framework of their zeros. A coherent framework was established by extending the study to related families, such as quantum-Hermite Bernoulli, quantum-Hermite Euler, and quantum-Hermite Genocchi polynomials. These discoveries enhance the knowledge of quantum polynomials and their relationships to classical and contemporary special functions.}
}