Identities involving values of Bernstein, \(q\)-Bernoulli, and \(q\)-Euler polynomials. (English) Zbl 1256.11013

Summary: In this paper, we give relations involving values of \(q\)-Bernoulli, \(q\)-Euler, and Bernstein polynomials. Using these relations, we obtain some interesting identities on the \(q\)-Bernoulli, \(q\)-Euler, and Bernstein polynomials.


11B68 Bernoulli and Euler numbers and polynomials
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
05A30 \(q\)-calculus and related topics
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