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

Abstract

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.