Certain Results for the Twice-Iterated 2D <i>q</i>-Appell Polynomials

Abstract

In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated.

Keywords

• 2d <i>q</i>-appell polynomials
• twice-iterated 2d <i>q</i>-appell polynomials
• determinant expressions
• recurrence relations
• 2d <i>q</i>-bernoulli polynomials
• 2d <i>q</i>-euler polynomials
• 2d <i>q</i>-genocchi polynomials
• apostol type bernoulli
• euler and genocchi polynomials