Abstract
The goal of this paper is to define the ( p , q ) -analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type q-tangent numbers and polynomials. We get some explicit formulas and properties in conjunction with ( p , q ) -analogue of tangent numbers and polynomials. We give some new symmetric identities for ( p , q ) -analogue of tangent polynomials by using ( p , q ) -tangent zeta function. Finally, we investigate the distribution and symmetry of the zero of ( p , q ) -analogue of tangent polynomials with numerical methods.
Highlights
The field of the special polynomials such as tangent polynomials, Bernoulli polynomials, Euler polynomials, and Genocchi polynomials is an expanding area in mathematics.Many generalizations of these polynomials have been studied
Migliorati and Srivastava derived a generalization of the classical polynomials
It is the purpose of this paper to introduce and investigate a new some generalizations of the Carlitz-type q-tangent numbers and polynomials, q-tangent zeta function, Hurwiz q-tangent zeta function
Summary
The field of the special polynomials such as tangent polynomials, Bernoulli polynomials, Euler polynomials, and Genocchi polynomials is an expanding area in mathematics (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]) Many generalizations of these polynomials have been studied (see [1,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18]). Migliorati and Srivastava derived a generalization of the classical polynomials (see [6]) It is the purpose of this paper to introduce and investigate a new some generalizations of the Carlitz-type q-tangent numbers and polynomials, q-tangent zeta function, Hurwiz q-tangent zeta function. The structure of the paper is as follows: In Section 2 we define Carlitz-type ( p, q)-tangent numbers and polynomials and derive some of their properties involving elementary properties, distribution relation, property of complement, and so on
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