Q-Binomial
From specialfunctionswiki
$${n \brack m}_q = \dfrac{(q;q)_n}{(q;q)m(q;q)_{n-m}},$$ where $(q;q)_k$ is the q-Pochhammer symbol.
Properties
Theorem: For $|x|<1,|q|<1$, $$\displaystyle\sum_{k=0}^{\infty} \dfrac{(a;q)_k}{(q;q)_k} x^k = \dfrac{(ax;q)_{\infty}}{(x;q)_{\infty}}.$$
Proof: proof goes here █
