Open Access

Some Relationships between the Analogs of Euler Numbers and Polynomials

Journal of Inequalities and Applications20072007:086052

https://doi.org/10.1155/2007/86052

Received: 5 June 2007

Accepted: 26 August 2007

Published: 30 October 2007

Abstract

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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Authors’ Affiliations

(1)
Department of Mathematics, Hannam University
(2)
School of Electronic Engineering and Computer Science, Kyungpook National University
(3)
Department of Mathematics and Computer Sciences, KonKuk University

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Copyright

© C. S. Ryoo et al. 2007

This article is published under license to BioMed Central Ltd. 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.