Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 807176, 11 pages
Research Article

A Note on the (h,q)-Extension of Bernoulli Numbers and Bernoulli Polynomials

1Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea
2Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 13 May 2010; Accepted 11 July 2010

Academic Editor: Leonid Shaikhet

Copyright © 2010 C. S. Ryoo and T. Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We observe the behavior of roots of the (h,q)-extension of Bernoulli polynomials Bn,q(h)(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials Bn,q(h)(x). The main purpose of this paper is also to investigate the zeros of the (h,q)-extension of Bernoulli polynomials Bn,q(h)(x). Furthermore, we give a table for the zeros of the (h,q)-extension of Bernoulli polynomials Bn,q(h)(x).