Determinant forms, difference equations and zeros of the \(q\)-Hermite-Appell polynomials
Summary: 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.
scientific article; zbMATH DE number 6994861
scientific article