A Numerical Computation of Zeros and Determinant Forms for Some New Families of q-special Polynomials

Abstract

The main aim of this article is to investigate some new families of q-special polynomials and to study their properties using different approaches. The 2-iterated q-Appell polynomial family is introduced and some properties of these polynomials are considered under q-umbral calculus methods. Some 2-iterated q-Appell and hybrid q-special polynomials are studied as members of this family. The numbers related to these polynomials are obtained. The graphical representation of the 2-iterated and hybrid q-Appell polynomials is presented. The zeros of these polynomials are investigated for some values of index n using numerical computation. The approximate solutions of the real zeros of these polynomials are also considered. The determinant forms for the 2-iterated q-Appell family and for the 2-iterated and hybrid q-special polynomials are established using linear algebraic approach.