Identities of symmetry for q-Bernoulli polynomials

TL;DR

This paper introduces eight new identities of symmetry involving three variables for q-Bernoulli polynomials and q-analogue power sums, expanding the understanding of symmetries beyond previous two-variable results.

Contribution

The paper presents novel three-variable symmetry identities for q-Bernoulli polynomials and q-power sums, derived from p-adic integral representations, advancing the theoretical framework.

Findings

Eight new symmetry identities in three variables

Enhanced understanding of symmetries in q-Bernoulli polynomials

Derivation based on p-adic integral methods

Abstract

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