Differential Equations Associated With Tangent Numbers

Abstract

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

Differential equations associated with generalized Bell polynomials and their zeros

“…Differential equations arising from the generating functions of special polynomials are studied by many authors in order to give explicit identities for special polynomials (see [11][12][13] …”

“…Recently, many mathematicians have studied the differential equations arising from the generating functions of special polynomials (see [11][12][13]). In this paper, we study differential equations arising from the generating functions of generalized Bell polynomials.…”

Differential Equations Arising from the 3-Variable Hermite Polynomials and Computation of Their Zeros

“…Many mathematicians have studied in the area of the Bernoulli numbers, Euler numbers, Genocchi numbers, and tangent numbers see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The special polynomials of two variables provided new means of analysis for the solution of a wide class of differential equations often encountered in physical problems.…”

“…Recently, many mathematicians have studied the differential equations arising from the generating functions of special polynomials (see [7,8,12,[16][17][18][19]). In this paper, we study differential equations arising from the generating functions of the 3-variable Hermite polynomials.…”

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.…”