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

Kim, Taekyun

J. Comput. Anal. Appl. 14, No. 5, 917-933 (2012).

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.

MSC:

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.)

Keywords:

\(q\)-Bernoulli polynomials; \(q\)-Bernstein polynomials; \(q\)-Stirling numbers