- Taekyun Kim
^{1}Email author, - Lee-Chae Jang
^{2}, - Young-Hee Kim
^{1}and - Kyung-Won Hwang
^{3}

**2009**:640152

https://doi.org/10.1155/2009/640152

© Taekyun Kim et al. 2009

**Received: **5 June 2009

**Accepted: **5 August 2009

**Published: **26 August 2009

## Abstract

## Keywords

## 1. Introduction

and the generalized Bernoulli numbers attached to , , are defined as (see [1–20, 25]). The purpose of this paper is to derive some identities of symmetry for the generalized Bernoulli polynomials attached to of higher order.

## 2. Symmetric Properties for the Generalized Bernoulli Polynomials of Higher Order

(see [25]).

From (2.16), we note that

By the symmetry of in and , we see that

By comparing the coefficients on the both sides of (2.17) and (2.18), we see the following theorem.

Theorem 2.1.

Remark 2.2.

(see [25]).

By comparing the coefficients on the both sides of (2.21) and (2.22), we obtain the following theorem.

Theorem 2.3.

Remark 2.4.

(see [25]).

## Declarations

### Acknowledgment

The present research has been conducted by the research Grant of the Kwangwoon University in 2009.

## Authors’ Affiliations

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