A $q$-analog of the Bailey-Borwein-Bradley identity

TL;DR

This paper develops a $q$-analogue of the Bailey-Borwein-Bradley identity, creating accelerated series for even zeta values and $q$-analogues of series for $rac{3}{2}$, using the $q$-Markov-WZ method.

Contribution

It introduces new $q$-analogues of classical identities and series for zeta values, expanding the mathematical framework for $q$-series and special functions.

Findings

Established a $q$-analogue of the Bailey-Borwein-Bradley identity.

Proved $q$-analogues of Markov's and Amdeberhan's series for $rac{3}{2}$.

Demonstrated the effectiveness of the $q$-Markov-WZ method.

Abstract

We establish a $q$-analogue of the Bailey-Borwein-Bradley identity generating accelerated series for even zeta values and prove $q$-analogues of Markov's and Amdeberhan's series for $\zeta(3)$ using the $q$-Markov-WZ method.