Certain Results of q-Sheffer-Appell Polynomials - Araci, Serkan; Muhyi, Abdulghani; Yasmin, Ghazala; Aracı, Serkan (MDPI, 2019)
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