Determinant approach to the 2-Iterated q-Appell and mixed type q-Appell polynomials

TL;DR

This paper introduces the 2-iterated q-Appell family of polynomials, explores their properties, provides determinant definitions, and investigates their roots through graphical and numerical methods.

Contribution

It presents the first systematic study of 2-iterated q-Appell polynomials, including their determinant representations and root analysis.

Findings

Determinant definitions for the 2-iterated q-Appell family are established.

Graphs and roots of these polynomials are analyzed using MATLAB.

Approximate solutions for the real zeros are provided.

Abstract

In this article, the 2-iterated q-Appell family is introduced. Certain 2-iterated q-Appell and mixed type q-special polynomials are considered as members of this family. The numbers related to these polynomials are obtained. The determinant definitions for the 2-iterated q-Appell family and for the 2-iterated and mixed type q-Appell polynomials are established. The graphs of some 2-iterated q-Appell and mixed type q-Appell polynomials are drawn for different values of indices and the roots of these polynomials are also investigated for certain values of index n by using Matlab. Finally, the approximate solutions of the real zeros of these polynomials are given.