Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 851521, 16 pages
Research Article

Identities of Symmetry for Euler Polynomials Arising from Quotients of Fermionic Integrals Invariant under S3

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

Received 16 February 2010; Accepted 13 April 2010

Academic Editor: Yeol J. E. Cho

Copyright © 2010 Dae San Kim and Kyoung Ho Park. 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.


We derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundances of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the p-adic integral expression of the generating function for the Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating power sums.