# Proving generating functions equality

What do you use to prove the following equality (and possibly more general ones of the kind)?

\begin{align*}\sum_{r,s,t} \frac{q^{r^2+rs+s^2+st+t^2}}{(q)_r (q)_s (q)_t} z_1^{r+s} z_2^{s+t} = \sum_{a,b} \frac{q^{a^2-ab+b^2}}{(q)_a (q)_b} z_1^a z_2^b \end{align*}

Thanks!

-
Note that the question was posted to MathOverflow, where some comments were made. – Gerry Myerson Jun 27 '12 at 0:39