We develop an analytical technique to derive explicit forms of thermodynami
cal quantities within the asymptotic approach to son-extensive quantum dist
ribution functions. Using it, we find an expression for the number of parti
cles in a boson system which we compare with other approximate scheme (i.e.
factorization approach), and with the recently obtained exact result. To d
o this, we investigate the predictions on Bose-Einstein condensation and th
e blackbody radiation. We find that both approximation techniques give resu
lts similar to (up to O(q-1)) the exact ones, making them a useful tool for
computations. Because of the simplicity of the factorization approach form
ulae, it appears that this is the easiest way to handle with physical syste
ms which might exhibit slight deviations from extensivity.