Abstract
In this article, we derive an asymptotic formula for the q-factorial number of order n using the saddle point method. This formula is a q-analogue, for 0 < q < 1, of the usual Stirling formula for the factorial number of order n. Also, this formula is used to provide a continuous limiting behaviour of the q-Binomial distribution in the sense of pointwise convergence. Specifically, the q-Binomial distribution converges to a continuous Stieltjes–Wigert distribution. Furthermore, we present some numerical calculations, using the computer program MAPLE, indicating a quite strong convergence.
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