Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 86052, 22 pages
Research Article

Some Relationships between the Analogs of Euler Numbers and Polynomials

C. S. Ryoo,1 T. Kim,2 and Lee-Chae Jang3

1Department of Mathematics, Hannam University, Daejeon 306-791, South Korea
2School of Electronic Engineering and Computer Science, Kyungpook National University, Taegu 702-701, South Korea
3Department of Mathematics and Computer Sciences, KonKuk University, Chungju 308-701, South Korea

Received 5 June 2007; Revised 28 July 2007; Accepted 26 August 2007

Academic Editor: Narendra K. Govil

Copyright © 2007 C. S. Ryoo et al. 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 construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet l-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials. By numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted q-Euler polynomials. Finally, we give a table for the solutions of the twisted q-Euler polynomials.