Abstract
In this paper, the authors discover some new symmetric identities of Carlitz's twisted q-Bernoulli polynomials arising from the p-adic q-integral on Zp under symmetric group of degree four shown by S4.
Highlights
As well known that the ordinary Bernoulli polynomials, Bn(x), are defined by the following Taylor series expansion about t = 0: ∞ Bn(x) tn n! = et t − 1 ext, n=0 (|t| < 2π). (1.1)Upon setting x = 0 in the Eq (1.1), we have Bn(0) := Bn that is popularly known as n-th Bernoulli number.Received: Febrauray 4, 2016Revised: Published: September 30, 2016
Throughout this paper, Zp, Q, Qp and Cp will denote the ring of p-adic rational integers, the field of rational numbers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, respectively
For ζ ∈ Tp, we indicate by φζ : Zp → Cp the locally constant function x → ζx
Summary
NOVEL IDENTITIES OF SYMMETRY FOR CARLITZ’S TWISTED q-BERNOULLI POLYNOMIALS UNDER S4. Ugur Duran1 §, Mehmet Acikgoz2 1,2Department of Mathematics Faculty of Arts and Science University of Gaziantep TR-27310 Gaziantep, TURKEY
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