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Some identities of the twisted \(q\)-Genocchi numbers and polynomials with weight \(\alpha\) and \(q\)-Bernstein polynomials with weight \(\alpha\). (English) Zbl 1232.11029

Summary: Recently mathematicians have studied some interesting relations between \(q\)-Genocchi numbers, \(q\)-Euler numbers, polynomials, Bernstein polynomials, and \(q\)-Bernstein polynomials. In this paper, we give some interesting identities of the twisted \(q\)-Genocchi numbers, polynomials, and \(q\)-Bernstein polynomials with weighted \(\alpha\).

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11B75 Other combinatorial number theory
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
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