Gaussian Binomial Theorem/Negation of Upper Index

Theorem
Let $r \in \R$ be a real number.

where:
 * $\dbinom r k_q$ denotes a Gaussian binomial coefficient.
 * $x \in \R: \left\lvert{x}\right\rvert < 1$
 * $q \in \R: \left\lvert{q}\right\rvert < 1$.