Research Article
Identities of Symmetry for Euler Polynomials Arising from Quotients of Fermionic Integrals Invariant under ![]()
Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Journal of Inequalities and Applications 2010, 2010:851521 doi:10.1155/2010/851521
Published: 20 May 2010Abstract
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 
-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.
