Abstract
Symmetric properties for the generalized (h, q)-tangent polynomials
Highlights
Euler numbers, Euler polynomials, Bernoulli numbers, Bernoulli polynomials, tangent numbers, and tangent polynomials possess many interesting properties and arise in many areas of mathematics and physics(see [1,2,3,4,5,6])
For g ∈ U D(Zp) the fermionic p-adic invariant integral on Zp is defined by Kim as follows: I−1(g) = g(x)dμ−1(x) = lim g(x)(−1)x
In [5], we introduced the generalized (h, q)-tangent numbers Tn(h,χ),q and polynomials Tn(h,χ),q(x) attached to χ
Summary
Euler polynomials, Bernoulli numbers, Bernoulli polynomials, tangent numbers, and tangent polynomials possess many interesting properties and arise in many areas of mathematics and physics(see [1,2,3,4,5,6]). Throughout this paper we use the following notations. By Zp we denote the ring of padic rational integers, Q denotes the field of rational numbers, Qp denotes the field of p-adic rational numbers, C denotes the complex number field, and Cp denotes the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p−νp(p) = p−1. Talks of q-extension, q is considered in many ways such as an indeterminate, a complex number q ∈ C, or p-adic number q ∈ Cp. If q ∈ C one normally assume that
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