  In this paper, 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 abundance 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.
