Determinant Forms, Difference Equations and Zeros of the <i>q</i>-Hermite-Appell Polynomials

Abstract

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

Keywords

• <i>q</i>-Appell polynomials
• <i>q</i>-Hermite polynomials
• <i>q</i>-Hermite-Appell polynomials
• <i>q</i>-recurrence relations
• <i>q</i>-difference equations