A New approach to q-zeta function

TL;DR

This paper introduces a novel q-extension of Bernoulli numbers and polynomials and explores the associated q-zeta functions that interpolate these new extensions.

Contribution

It presents a new q-analogue of Bernoulli numbers and polynomials along with the corresponding q-zeta functions, expanding the mathematical framework.

Findings

Defined new q-extensions of Bernoulli numbers and polynomials

Constructed q-zeta functions interpolating these new extensions

Provides foundational tools for further q-analogue research

Abstract

We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.