Gaussian Binomial Theorem

Theorem

 * $\displaystyle \prod_{k \mathop = 1}^n \left({1 + q^{k - 1} x}\right) = \sum_{k \mathop \in \Z} \dbinom n k_q q^{k \left({k - 1}\right) / 2} x^k$

where $\dbinom n k_q$ denotes a Gaussian binomial coefficient.