International Journal of Combinatorics
Volume 2011 (2011), Article ID 432738, 12 pages
doi:10.1155/2011/432738
Research Article

Identities of Symmetry for Generalized Euler Polynomials

Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea

Received 10 January 2011; Accepted 15 February 2011

Academic Editor: Chính T. Hoang

Copyright © 2011 Dae San 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

We derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the 𝑝 -adic fermionic integral expression of the generating function for the generalized Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized power sums.