Identities of symmetry for generalized Bernoulli polynomials

TL;DR

This paper introduces eight new identities of symmetry involving three variables for generalized Bernoulli polynomials and power sums, expanding previous two-variable results using p-adic integral methods.

Contribution

It presents novel three-variable symmetry identities for generalized Bernoulli polynomials and power sums, derived via p-adic integral techniques, extending prior two-variable findings.

Findings

Eight new symmetry identities in three variables

Derived using p-adic integral expressions

Extends previous two-variable symmetry results

Abstract

In this paper, we derive eight basic identities of symmetry in three variables related to generalized Bernoulli polynomials and 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 integral expression of the generating function for the generalized Bernoulli polynomials and the quotient of $p$-adic integrals that can be expressed as the exponential generating function for the generalized power sums.