$q$-Analogues of some series for powers of $π$

We obtain $q$-analogues of several series for powers of $π$. For example, the identity $\sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)^3}=\frac{π^3}{32}$ has the following $q$-analogue: \begin{equation*} \sum_{k=0}^\infty(-1)^k\frac{q^{2k}(1+q^{2k+1})}{(1-q^{2k+1})^3}=\frac{(q^2;q^4)_{\infty}^2(q^4;q^4)_{\infty}^6} {(q;q^2)_{\infty}^4}, \end{equation*} where $q$ is any complex number with $|q|<1$. We also give $q$-analogues of four new series for powers of $π$ found by the second author.

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