@article{Fadel2026, 
author = {Mohammed Fadel and Ugur Duran and Clemente Cesarano and William Ramírez},
title = {Determinant approach of the    (  p  ,  q  )-Hermite-Appell polynomials and some of their components},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {1},
pages = {70-91},
keywords = {(p, q)-polynomials, (p, q)-Appell polynomials, (p, q)-Hermite polynomials, determinant approach},
url = {https://www.sciopen.com/article/10.3934/nhm.2026004},
doi = {10.3934/nhm.2026004},
abstract = {In this work, we offer the novel class of    (      p    ,      q    )-Hermite-Appell polynomials. Some attributes of this class are constructed, along with the generating function, series definition,    (      p    ,      q    )-derivative properties,    (      p    ,      q    )-integral representation, summation formulas, and determinate representation. Additionally, we consider a few components for the    (      p    ,      q    ) -Hermite-Appell polynomials and infer certain elements of their traits. The generating function and series expansions of some classes of two-dimensional    (      p    ,      q    )-Hermite-Appell polynomials are provided. Moreover, we acquire a    (      p    ,      q    )-differential operator formula for    (      p    ,      q    )-Hermite-Appell polynomials. Finally, the Wolfram Mathematica software is used to plot the graphical diagrams of select components of    (      p    ,      q    )-Hermite-Appell, along with two-dimensional    (      p    ,      q    )-Hermite-Appell polynomials.}
}