Open Access Research Article

Some Relationships between the Analogs of Euler Numbers and Polynomials

CS Ryoo1*, T Kim2 and Lee-Chae Jang3

Author Affiliations

1 Department of Mathematics, Hannam University, Daejeon 306-791, South Korea

2 School of Electronic Engineering and Computer Science, Kyungpook National University, Taegu 702-701, South Korea

3 Department of Mathematics and Computer Sciences, KonKuk University, Chungju 308-701, South Korea

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Journal of Inequalities and Applications 2007, 2007:086052 doi:10.1155/2007/86052


The electronic version of this article is the complete one and can be found online at: http://www.journalofinequalitiesandapplications.com/content/2007/1/086052


Received:5 June 2007
Revisions received:28 July 2007
Accepted:26 August 2007
Published:30 October 2007

© 2007 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 -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 -Euler polynomials. Finally, we give a table for the solutions of the twisted -Euler polynomials.

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