Abstract
We consider q-binomial coefficients built from the q-rational and q-real numbers defined by Morier-Genoud and Ovsienko in terms of continued fractions. We establish versions of both the q-Pascal identity and the q-binomial theorem in this setting. These results are then used to find more identities satisfied by the q-analogues of Morier-Genoud and Ovsienko, including a Chu–Vandermonde identity and q-Gamma function identities.
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