Rota-Baxter operators and Bernoulli polynomials

TL;DR

This paper explores the relationship between Rota-Baxter operators and Bernoulli polynomials, revealing how operator properties lead to polynomial identities and symmetries.

Contribution

It establishes a novel connection between Rota-Baxter operators and Bernoulli polynomials, deriving new identities and symmetry properties.

Findings

Rota-Baxter operator properties imply Bernoulli polynomial symmetries

Operator equalities generate identities for Bernoulli polynomials

Connection enhances understanding of algebraic structures in mathematical physics

Abstract

We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the last.