q-Euler numbers and polynomials associated with multiple q-zeta functions

TL;DR

This paper systematically studies families of multiple q-Euler numbers and polynomials, and constructs multiple q-zeta functions that interpolate these numbers at negative integers.

Contribution

It introduces a new framework connecting multiple q-Euler numbers and polynomials with multiple q-zeta functions, expanding the theoretical understanding.

Findings

Defined multiple q-Euler numbers and polynomials.

Constructed multiple q-zeta functions interpolating at negative integers.

Established relationships between these functions and classical q-analogs.

Abstract

The purpose this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials and we construct multiple q-zeta function which interpolates multiple q-Euler numbers at negative integers.