Explicit properties of apostol-type frobenius-euler polynomials involving q-trigonometric functions with applications in computer modeling

Abstract

In this article, we define q-cosine and q-sine Apostol-type Frobenius-Euler polynomials and derive interesting relations. We also obtain new properties by making use of power series expansions of q-trigonometric functions, properties of q-exponential functions, and q-analogues of the binomial theorem. By using the Mathematica program, the computational formulae and graphical representation for the aforementioned polynomials are obtained. By making use of a partial derivative operator, we derived some interesting finite combinatorial sums. Finally, we detail some special cases for these results