Identities of symmetry for higher-order Euler polynomials in three variables (II)

Abstract

We derive twenty five basic identities of symmetry in three variables related to higher-order Euler polynomials and alternating power sums. This demonstrates that there are abundant identities of symmetry in three-variable case, in contrast to two-variable case, where there are only a few. These are all new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the higher-order Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating power sums.