Barnes type multiple q-zeta functions and q-Euler polynomials

TL;DR

This paper introduces a q-analogue of Barnes multiple zeta functions and higher-order Euler polynomials, expanding their applications in number theory, knot theory, and mathematical physics.

Contribution

It develops a new q-extension of Barnes multiple zeta functions and constructs q-extensions of Euler polynomials of higher order, advancing the theoretical framework.

Findings

Defined q-extensions of Barnes multiple zeta functions

Constructed q-extensions of higher-order Euler polynomials

Potential applications in number theory and mathematical physics

Abstract

The Barnes multiple zeta function is useful to study in the number theory and Knot thoey and Mathematical Physics. In this paper we consider q-extension of Barnes type multiple zeta function and we also construct the q-extension of Euler polynomials of higher order