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.
Keywords and phrases
q-binomial distribution discrete normal distribution Heine distribution q-Krawtchouk polynomials q-Charlier polynomials Mellin transform limit theorems
AMS (2000) subject classification
Primary 60F05 secondary 33D15
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