1029-242X-2007-086052 1029-242X Research Article <p>Some Relationships between the Analogs of Euler Numbers and Polynomials</p> RyooCSryoocs@hannam.ac.kr KimTtkim@knu.ac.kr JangLee-Chaeleechae.jang@kku.ac.kr

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

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

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

 Journal of Inequalities and Applications 1029-242X 2007 2007 1 086052 http://www.journalofinequalitiesandapplications.com/content/2007/1/086052 10.1155/2007/86052 5620072872007268200730102007 2007Ryoo 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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