Hi I am wondering if there is a general procedure (perhaps for a specific class) simplifying q-series of the form $(q^a;q^{na})_{\infty}$ where $n\in \mathbb{Z}^{+}$, into the product/qoutient of q-series which are of the form $(q^b;q^b)_{\infty}$ . I know that $(q^2;q^4)_{\infty} = \frac{ (q^2;q^2)_{\infty}}{(q^4;q^4)_{\infty} }.$
I have several q-series like $(q^2;q^6)_{\infty}$ and $(q^{10};q^2)_{\infty}$, to name a few, which I need to simplify.
Thanks