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On Continuous Limiting Behaviour for the q(n)-Binomial Distribution with q(n)→1 as n→∞

Recently, Kyriakoussis and Vamvakari [1] have established a q-analogue of the Stirling type for q-constant which have lead them to the proof of the pointwise convergence 
of the q-binomial distribution to a 
Stieltjes-Wigert continuous distribution. In the present article, assuming a sequence q(n) of n with q(n)→1 as n→∞, the study of the 
affect of this assumption to the q(n)-analogue of the 
Stirling type and to the asymptotic behaviour of the q(n)-Binomial distribution 
is presented. Specifically, a q(n) analogue of the Stirling type is provided 
which leads to the proof of deformed Gaussian limiting behaviour for the q(n)-Binomial 
distribution. Further, figures using the program MAPLE are presented, 
indicating the accuracy of the established distribution convergence even for 
moderate values of n.