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

Abstract

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 non-archimedean combinatorial analysis.