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Determinant Forms, Difference Equations and Zeros of the <i>q</i>-Hermite-Appell Polynomials
oleh: Subuhi Khan, Tabinda Nahid
Format: | Article |
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Diterbitkan: | MDPI AG 2018-11-01 |
Deskripsi
The present paper intends to introduce the hybrid form of <i>q</i>-special polynomials, namely <i>q</i>-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of <i>q</i>-Hermite-Appell polynomials such as determinant definitions, <i>q</i>-recurrence relations and <i>q</i>-difference equations are established. Examples providing the corresponding results for certain members belonging to this <i>q</i>-Hermite-Appell family are considered. In addition, graphs of certain <i>q</i>-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these <i>q</i>-special polynomials is displayed.