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The  q -Bernstein basis used to construct the  q -Bernstein polynomials is an extension of the Bernstein basis related to the  q -binomial probability distribution. This distribution plays a profound role in the  q -boson operator calculus. In the case  q  &gt; 1,  q -Bernstein basic polynomials on [0, 1] combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of  q -Bernstein polynomials in the case of  q  &gt; 1.

On the q -Bernstein polynomials of the logarithmic function in the case q > 1