Multiple Twisted q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals

Lee-Chae Jang

doi:10.1155/2008/738603

Abstract

By using -adic -integrals on , we define multiple twisted -Euler numbers and polynomials. We also find Witt's type formula for multiple twisted -Euler numbers and discuss some characterizations of multiple twisted -Euler Zeta functions. In particular, we construct multiple twisted Barnes' type -Euler polynomials and multiple twisted Barnes' type -Euler Zeta functions. Finally, we define multiple twisted Dirichlet's type -Euler numbers and polynomials, and give Witt's type formula for them.

Highlights

Let p be a fixed odd prime number
When one talks about q-extension, q is variously considered as an indeterminate, a complex number, q ∈ C or a p-adic number q ∈ Cp
If q ∈ C, one normally assumes that |q| < 1

Summary

Introduction

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp are, respectively, the ring of p-adic rational integers, the field of p-adic rational numbers, and the p-adic completion of the algebraic closure of Qp. A dpZp , 0

Multiple twisted q-Euler numbers and polynomials

Multiple twisted q-Euler Zeta functions

Multiple twisted Barnes’ type q-Euler polynomials

Multiple twisted Dirichlet’s type q-Euler numbers and polynomials