Dixon's Identity/Gaussian Binomial Form/Formulation 2

Theorem
For $l, m, n \in \Z_{\ge 0}$:


 * $\ds \sum_{k \mathop \in \Z} \paren {-1}^k \dbinom {l + m} {l + k}_q \dbinom {m + n} {m + k}_q \dbinom {n + l} {n + k}_q = \dfrac {\paren {l + m + n}!_q} {l!_q \, m!_q \, n!_q}$

where:
 * $\dbinom {l + m} {l + k}_q$ denotes a Gaussian binomial coefficient
 * $l!_q$ is defined as $\ds \prod_{k \mathop = 1}^n \paren {1 + q + \cdots + q^{k - 1} }$