International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 424189, 7 pages
http://dx.doi.org/10.1155/2012/424189
Research Article

Symmetry Fermionic 𝑝 -Adic 𝑞 -Integral on ℤ 𝑝 for Eulerian Polynomials

Daeyeoul Kim1 and Min-Soo Kim2

1National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of Korea
2Division of Cultural Education, Kyungnam University, Changwon 631-701, Republic of Korea

Received 18 June 2012; Accepted 14 August 2012

Academic Editor: Cheon Ryoo

Copyright © 2012 Daeyeoul Kim and Min-Soo Kim. 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

Kim et al. (2012) introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on ℤ 𝑝 , defined by Kim (2008), we show a symmetric relation between the q-extension of the alternating sum of integer powers and the Eulerian polynomials.