Certain Results of q -Sheffer–Appell Polynomials

Abstract

In this paper, the class of q -Sheffer–Appell polynomials is introduced. The generating function, series definition, determinant definition and some other identities of this class are established. Certain members of q -Sheffer–Appell polynomials are investigated and some properties of these members are derived. In addition, the class of 2D q -Sheffer–Appell polynomials is introduced. Further, the graphs of some members of q -Sheffer–Appell polynomials and 2D q -Sheffer–Appell polynomials are plotted for different values of indices by using Matlab.

Keywords

• q -Sheffer–Appell polynomials
• generating relations
• determinant definition
• recurrence relation
• q -Hermite–Bernoulli polynomials
• q -Hermite–Euler polynomials
• q -Hermite–Genocchi polynomials