Identities of symmetry for generalized Euler polynomials

TL;DR

This paper introduces eight new symmetry identities involving generalized Euler polynomials and alternating power sums in three variables, expanding the existing two-variable symmetry results using p-adic integral techniques.

Contribution

It presents novel three-variable symmetry identities for generalized Euler polynomials, derived through p-adic integral methods, extending prior two-variable results.

Findings

Eight new symmetry identities in three variables

Derived using p-adic fermionic integrals

Extends previous two-variable symmetry results

Abstract

In this paper, we derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the $p$-adic fermionic integral expression of the generating function for the generalized Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized power sums.