Abstract
In this paper, we consider the Barnes-type q-Euler polynomials which are derived from the fermionic p-adic q-integrals and investigate some identities of these polynomials. Furthermore, we define the Barnes-type q-Changhee polynomials and numbers, and we derive some identities related with the Barnes-type q-Euler polynomials and the Barnes-type q-Changhee polynomials.
Highlights
Let p be a fixed odd prime number
The main results of this paper are some identities of the Barnes-type q-Euler polynomials
We define the Barnes-type q-Changhee polynomials and numbers, and we derive some identities related with the Barnes-type q-Euler polynomials and the Barnes-type q-Changhee polynomials
Summary
Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will, respectively, denote the rings of p-adic integers, the fields of p-adic numbers, and the completion of the algebraic closure of Qp. ∈ C(Zp), the fermionic p-adic integral on Zp is defined by Kim, I–q(f ) = We note that limq→ En,q(x) = En(x), where En(x) are called the Euler polynomials which are defined by the generating function, et tn En(x) n! In [ ], Kim ( ) presented the generating functions related to the q-Euler polynomials of higher order and gave some interesting identities involving these polynomials.
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