SIAM JOURNAL ON DISCRETE MATHEMATICS, cilt.28, sa.3, ss.1009-1025, 2014 (SCI-Expanded)
We derive explicit formulas for the generating functions of the q-Bernstein basis functions in terms of q-exponential functions. Using these explicit formulas, we derive a collection of functional equations for these generating functions which we apply to prove a variety of identities, some old and some new, for the q-Bernstein bases.