Rota-Baxter operators and Bernoulli polynomials

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.

13 p; v2: references to the works of Miller and Ogievetsky & Schechtman were added

References in corpus (2)

• Loday-type Algebras and the Rota-Baxter Relation
• On embedding of dendriform algebras into Rota---Baxter algebras