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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 298531, 11 pages
http://dx.doi.org/10.1155/2012/298531
Research Article

Explicit Formulas Involving -Euler Numbers and Polynomials

1Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey
2Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 4 April 2012; Accepted 4 October 2012

Academic Editor: Gerd Teschke

Copyright © 2012 Serkan Araci 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.

Abstract

We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator. Also, we derive relations between the -Euler numbers and -Bernoulli numbers via the -adic -integral in the -adic integer ring.