@article{Zayed2024, 
author = {Mohra Zayed and Shahid Ahmad Wani},
title = {Properties and applications of generalized 1-parameter 3-variable Hermite-based Appell polynomials},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {25145-25165},
keywords = {1-parameter generalized Hermite polynomials, Appell polynomials, determinant definition, recurrence relations, differential equations},
url = {https://www.sciopen.com/article/10.3934/math.20241226},
doi = {10.3934/math.20241226},
abstract = {We present a novel framework for introducing generalized 3-variable 1-parameter Hermite-based Appell polynomials. These polynomials are characterized by generating function, series definition, and determinant definition, elucidating their fundamental properties. Moreover, utilizing a factorization method, we established recurrence relations, shift operators, and various differential equations, including differential, integrodifferential, and partial differential equations. Special attention is given to exploring the specific cases of 3-variable 1-parameter generalized Hermite-based Bernoulli, Euler, and Genocchi polynomials, offering insights into their unique features and applications.}
}