Abstract
We consider weighted -Genocchi numbers and polynomials. We investigated some interesting properties of the weighted -Genocchi numbers related to weighted -Bernstein polynomials by using fermionic -adic integrals on .
Highlights
1 − x n−k, and we obtain the classical Bernstein polynomials see 13, 14, where x q is a q-extension of x which is defined by 1 − qx x q 1−q, 1.3 see 1–4, 7, 9–12, 14–26
In this paper we obtained some relations between the weighted q-Bernstein polynomials and the q-Genocchi numbers
We derive some interesting identities on the q-Genocchi numbers and polynomials with weight α
Summary
K, n ∈ N∗ and x ∈ 0, 1 , Kim et al defined weighted q-Bernstein polynomials as follows: Bkα,n x, q n k x k qα 1−x n−k q−α. 1 − x n−k, and we obtain the classical Bernstein polynomials see 13, 14 , where x q is a q-extension of x which is defined by 1 − qx x q 1−q , 1.3 see 1–4, 7, 9–12, 14–26. Araci et al defined weighted q-Genocchi polynomials as follows: Gnα 1,q x n1 x y n qα dμ−q y. Araci et al defined q-Genocchi numbers with weight α as follows:. In this paper we obtained some relations between the weighted q-Bernstein polynomials and the q-Genocchi numbers. By the definition of q-Genocchi polynomials with weight α, we get x y n qα dμ−q y
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
