In this paper we introduce the tangent numbers T n and polynomials T n (x). Some interesting results and relationships are obtained.

Abstract:In this paper, we study some special polynomials which are related to Euler and Bernoulli polynomials. In addition, we give some identities for these polynomials. Finally, we investigate the zeros of these polynomials by using the computer.

In this paper, we study differential equations arising from the generating functions of tangent numbers. We give explicit identities for the tangent numbers.

In this paper, we observe the behavior of complex roots of the tangent polynomials Tn(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the tangent polynomials Tn(x). Finally, we give a table for the solutions of the tangent polynomials Tn(x).

No abstract