Abstract
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.
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Gerhold, S., Zeiner, M. Convergence properties of Kemp’s q-binomial distribution. Sankhya A 72, 331–343 (2010). https://doi.org/10.1007/s13171-010-0019-0
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DOI: https://doi.org/10.1007/s13171-010-0019-0