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