$q$-Rational and $q$-Real Binomial Coefficients
Combinatorics
2023-01-20 v1 Quantum Algebra
Abstract
We consider -binomial coefficients built from the -rational and -real numbers defined by Morier-Genoud and Ovsienko in terms of continued fractions. We establish versions of both the -Pascal identity and the -binomial theorem in this setting. These results are then used to find more identities satisfied by the -analogues of Morier-Genoud and Ovsienko, including a Chu--Vandermonde identity and -Gamma function identities.
Cite
@article{arxiv.2301.08185,
title = {$q$-Rational and $q$-Real Binomial Coefficients},
author = {John Machacek and Nicholas Ovenhouse},
journal= {arXiv preprint arXiv:2301.08185},
year = {2023}
}