Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q-Trigonometric Functions with Applications in Computer Modeling

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