Some formulae for the \(q\)-Bernstein polynomials and \(q\)-deformed binomial distributions. (English) Zbl 1256.11010

Summary: In this paper, we give new identities involving \(q\)-Bernstein polynomials and we derive some interesting properties of \(q\)-Bernstein polynomials associated with \(q\)-deformed binomial distributions.


11B65 Binomial coefficients; factorials; \(q\)-identities
11B68 Bernoulli and Euler numbers and polynomials
11B73 Bell and Stirling numbers
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)