Some identities on the q-tangent polynomials and Bernstein polynomials

Abstract

In this paper, we investigate some properties for the q-tangent numbers and polynomials. By using these properties, we give some interesting identities on the q-tangent polynomials and Bernstein polynomials. Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute