A $q$-analogue for Euler's $\zeta(6)=\pi^6/945$

TL;DR

This paper introduces a $q$-analogue of Euler's zeta value at 6, providing new formulas that connect $q$-series with classical constants like pi.

Contribution

It presents novel $q$-series representations for $ zeta(6)$, extending classical results to the $q$-analogue setting.

Findings

Derived explicit $q$-series formulas for $ zeta(6)$

Established connections between $q$-series and $rac{ extpi^6}{945}$

Provided theorems detailing the $q$-analogue structure

Abstract

We give a $q$-analogue of $\zeta(6)=\pi^6/945$. Our main results are stated in Theorems 2.1 and 2.2 below.