Abstract
In this paper, we consider the twisted Carlitz's q-Bernoulli numbers using p-adic q-integral on ℤ p . From the construction of the twisted Carlitz's q-Bernoulli numbers, we investigate some properties for the twisted Carlitz's q-Bernoulli numbers. Finally, we give some relations between the twisted Carlitz's q-Bernoulli numbers and q-Bernstein polynomials.
Highlights
Introduction and preliminariesLet p be a fixed prime number
Using p-adic q-integral equation on Zp, we investigate the properties of the twisted q-Bernoulli numbers and polynomials related to q-Bernstein polynomials
We derive some new identities for the twisted q-Bernoulli numbers and polynomials
Summary
Using p-adic q-integral equation on Zp, we investigate the properties of the twisted q-Bernoulli numbers and polynomials related to q-Bernstein polynomials. From these properties, we derive some new identities for the twisted q-Bernoulli numbers and polynomials. Final purpose of this paper is to give some relations between the twisted Carlitz’s q-Bernoulli numbers and q-Bernstein polynomials. 2. On the twisted Carlitz ‘s q-Bernoulli numbers we assume that n Î Z+, ξ Î Tp and q ∈ Cp with |1 - q|p < 1. Let us consider the nth twisted Carlitz’s q-Bernoulli polynomials using p-adic qintegral on Zp as follows: βn,ξ,q(x) = [y + x]nq ξ ydμq(y)
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