Explicit identities for the generalized tangent polynomials

Abstract

Recently, mathematicians have studied in the area of the Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi numbers and polynomials, and tangent numbers and polynomials(see [1, 3, 4, 6, 7, 8, 9]). We first give the definitions of the tangent numbers and polynomials. It should be mentioned that the definition of tangent numbers Tn and polynomials Tn(x) can be found in [4]. The tangent numbers Tn and polynomials Tn(x) are defined by means of the generating functions: