Mathematics, Vol. 11, Pages 2386: Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q-Trigonometric Functions with Applications in Computer Modeling

Mathematics, Vol. 11, Pages 2386: Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q-Trigonometric Functions with Applications in Computer Modeling

Mathematics doi: 10.3390/math11102386

Authors: Yongsheng Rao Waseem Ahmad Khan Serkan Araci Cheon Seoung Ryoo

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.