Title: Convergence Properties of Kemp’s q-Binomial Distribution
Author(s): Stefan Gerhold and Martin Zeiner
Pages: 331 -- 343
We consider Kemp's $q$-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are $q$-analogues of classical convergence properties. From the results about distributions, we deduce some new convergence results for ($q$-)Krawtchouk and $q$-Charlier polynomials. Besides elementary estimates, we apply Mellin transform asymptotics.