Symmetry identites for generalized twisted Euler polynomials twisted by ramified roots of unity

TL;DR

This paper introduces eight new symmetry identities involving generalized twisted Euler polynomials and power sums in three variables, expanding the understanding of their properties twisted by ramified roots of unity.

Contribution

It presents novel three-variable symmetry identities for generalized twisted Euler polynomials, extending previous two-variable results using p-adic integral techniques.

Findings

Eight new symmetry identities derived

Identities involve three variables and ramified roots of unity

Based on p-adic integral representations

Abstract

We derive eight identities of symmetry in three variables related to generalized twisted Euler polynomials and alternating generalized twisted power sums, both of which are twisted by ramified roots of unity. 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 integral expression of the generating function for the generalized twisted Euler polynomials and the quotient of $p$-adic integrals that can be expressed as the exponential generating function for the alternating generalized twisted power sums.