On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q =−1

The purpose of this paper is to construct λ-Euler numbers and polynomials by using fermionic expression of p-adic q-integral at q =−1. From these λ-Euler polynomials, we derive the harmonic sums of higher order. Finally, we investigate several interesting properties and relationships involving the classical as well as the generalized Euler numbers and polynomials. As an application, we will treat p-adic invariant integrals on Zp involving trigonometric functions. © 2006 Elsevier Inc. All rights reserved.