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Some identities on the \(q\)-Bernstein polynomials, \(q\)-Stirling numbers and \(q\)-Bernoulli numbers. (English) Zbl 1262.11020

Summary: In this paper we consider the \(q\)-Bernstein polynomials on \(\mathbb Z_p\) and investigate some interesting properties of these polynomials related to \(q\)-Stirling numbers and Carlitz’s type \(q\)-Bernoulli numbers.

MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities
11B68 Bernoulli and Euler numbers and polynomials
11B73 Bell and Stirling numbers
05A30 \(q\)-calculus and related topics
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