In the analysis of the structure of totally categorical first order theories, the second author showed that certain combinatorial counting functions play an important role. Those functions are invariants of the structures and are always polynomials in one or many variables, depending on the number of independent dimensions of the theory in question. The first author introduced the notion of gra...

In this paper, the Fourier series expansion of Tangent polynomials higher order is derived using Cauchy residue theorem. Moreover, some variations higher-order are defined by mixing concept with that Bernoulli and Genocchi polynomials, Tangent–Bernoulli Tangent–Genocchi polynomials. Furthermore, expansions these also