## 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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### References:

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