An invariant p-adic q-integral associated with q-Euler numbers and polynomials

The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf.[1,3,6,12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using multivariate p-adic q-integrals.These sums help us to study the relationships between p-adic q-integrals and nonarchimedean combinatorial analysis.