Some Identities on the q-Tangent Polynomials and Bernstein Polynomials
نویسنده
چکیده
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 closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute
منابع مشابه
Some Identities on the (h, q)-Tangent Polynomials and Bernstein Polynomials
In this paper, we investigate some properties for the (h, q)-tangent numbers and polynomials. By using these properties, we obtain some interesting identities on the (h, 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 o...
متن کاملModified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...
متن کاملSome identities on the weighted q-Euler numbers and q-Bernstein polynomials
Recently, Ryoo introduced the weighted q-Euler numbers and polynomials which are a slightly different Kim’s weighted q-Euler numbers and polynomials(see C. S. Ryoo, A note on the weighted q-Euler numbers and polynomials, 2011]). In this paper, we give some interesting new identities on the weighted q-Euler numbers related to the q-Bernstein polynomials 2000 Mathematics Subject Classification 11...
متن کاملThe Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials
In this paper, we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays. Constant or pantograph delays may appear in state-control or both. We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then, these are utilized to reduce the solution of optimal control with constant...
متن کاملSome Identities on the q - Bernoulli Numbers and Polynomials with Weight 0
and Applied Analysis 3 where n, k ∈ Z see 1, 9, 10 . For n, k ∈ Z , the p-adic Bernstein polynomials of degree n are defined by Bk,n x k x k 1 − x n−k for x ∈ Zp, see 1, 10, 11 . In this paper, we consider Bernstein polynomials to express the p-adic q-integral on Zp and investigate some interesting identities of Bernstein polynomials associated with the q-Bernoulli numbers and polynomials with ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013