Some Identities on Bernstein Polynomials Associated with -Euler Polynomials

Some Identities on the q-Tangent Polynomials and Bernstein Polynomials

In this paper, we investigate some properties for the q-tangent numbers and polynomials. By using these properties, we give some interesting identities on the q-tangent polynomials and Bernstein polynomials. Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic ...

Some Identities on the Twisted (h, q)-Genocchi Numbers and Polynomials Associated with q-Bernstein Polynomials

Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of padic rational integer, Qp denotes the ring of p-adic rational numbers, and Cp denotes the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N {0}. Let Cpn {ζ | ζpn 1} be the cyclic g...

Some Identities on the q-Euler Numbers with Weak Weight α and Bernstein Polynomials

In this paper we investigate some relations between Bernstein polynomials and q-Euler numbers with weak weight α. From these relations, we derive some interesting identities on the q-Euler numbers with weak weight α. Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of p-adic rati...

Some Identities of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials

Some Identities of the Frobenius-Euler Polynomials

and Applied Analysis 3 If n ∈ Nwith n ≡ 0 mod 2 , then we have I−1 fn − I−1 f 2 n−1 ∑ l 0 −1 l−1f l . 2.6 From 1.4 and 2.3 , we derive ∫ Zp eqdμ−1 x 2 2 q 1 − −q −1 et − −q −1 2 2 q ∞ ∑ n 0 Hn −q−1 t n n! . 2.7 Thus, we note that ∫ Zp xqdμ−1 x 2 2 q Hn −q−1 , ∫ Zp y x qdμ−1 x 2 2 q Hn −q−1, x . 2.8 Let n ∈ N with n ≡ 1 mod 2 . Then we obtain 2 q n−1 ∑ l 0 −1 ql qHm −q−1, n Hm −q−1 . 2.9 For n ∈...