- Lee-Chae Jang
^{1}Email author, - Won-Joo Kim
^{2}and - Yilmaz Simsek
^{3}

**2010**:163217

https://doi.org/10.1155/2010/163217

© Lee-Chae Jang et al. 2010

**Received: **13 August 2010

**Accepted: **15 September 2010

**Published: **19 September 2010

## Abstract

## 1. Introduction

for , where is called Bernstein polynomial of degree . Some researchers have studied the Bernstein polynomials in the area of approximation theory (see [1–6]).

In this paper, we consider Bernstein polynomials on and we investigate some interesting properties of Bernstein polynomials related to Stirling numbers and Bernoulli numbers.

## 2. Bernstein Polynomials Related to Stirling Numbers and Bernoulli Numbers

By (2.11), we obtain the following theorem.

Theorem 2.1.

where are the th Bernoulli numbers.

for . By (2.15), we obtain the following theorem.

Theorem 2.2.

By (2.17), (2.19), and (2.20), we obtain the following theorem.

Theorem 2.3.

By Theorems 2.2 and 2.3, we obtain the following corollary.

Corollary 2.4.

## Declarations

### Acknowledgment

The present investigation was supported by the Scientific Research Project Administration of Akdeniz University.

## Authors’ Affiliations

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## Copyright

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