A note on the tangent numbers and polynomials

Abstract

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

On the Generalized Degenerate Tangent Numbers and Polynomials

“…n T x (see [6]). For more theoretical properties of the generalized tangent numbers and polynomials, the readers may refer to [7].…”

A note on the symmetric properties for the q-twisted tangent polynomials

“…where T j,ω (x) and T j,ω denote the twisted tangent polynomials and the twisted tangent numbers, respectively(see [3]).…”

Dynamics of the zeros of analytic continued polynomials and differential equations associated with q-tangent polynomials

“…Using software algorithm, researchers can explore theoretical concepts and numerical experiments much more easily than in the past. There have been lots of research by mathematician in different kinds of the Tangent, Euler, Bernoulli, and Genocchi numbers and polynomials (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Numerical developments as well as experiments of Bernoulli polynomials, Euler polynomials, Genocchi polynomials, and Tangent polynomials have been studied with the significant progress in mathematics and computer science as one of the interesting subjects for the development of computer algorithms.…”

“…One can observe that if q → 1, then T n,q (x) = T n (x) and T n,q = T n (see [10]). As is well known that when m = 2 a special Bernoulli equation…”