Barnes-type multiple q-zeta functions and q-Euler polynomials**The present research has been conducted by the research grant of Kwangwoon University in 2010.

Abstract

The purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials and we construct multiple q-zeta functions which interpolate multiple q-Euler numbers at a negative integer. This is a partial answer to the open question in a previous publication (see Kim et al 2001 J. Phys. A: Math. Gen. 34 7633–8).