Some identities of degenerate Euler polynomials associated with degenerate Bernstein polynomials

Some identities of degenerate Fubini polynomials arising from differential equations

Recently, Kim et al. have studied degenerate Fubini polynomials in [T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, J. Nonlinear Sci. Appl., 9 (2016), 2857–2864]. Jang and Kim presented some identities of Fubini polynomials arising from differential equations in [G.-W. Jang, T. Kim, Adv. Studies Contem. Math., 28 (2018), to appear]. In this paper, we drive differential equations from the generating ...

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 of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials

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 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 ∈...