A symbolic approach to some identities for Bernoulli-Barnes polynomials

Lin Jiu , Victor H. Moll (1) , Christophe Vignat (2)

1 Department of Mathematics [Tulane, New Orleans]
2 L2S - Laboratoire des signaux et systèmes

The Bernoulli–Barnes polynomials are defined as a natural multidimensional extension of the classical Bernoulli polynomials. Many of the properties of the Bernoulli polynomials admit extensions to this new family. A specific expression involving the Bernoulli–Barnes polynomials has recently appeared in the context of self-dual sequences. The work presented here provides a proof of this self-duality using the symbolic calculus attached to Bernoulli numbers and polynomials. Several properties of the Bernoulli–Barnes polynomials are established by this procedure.

Domains: Probability [math.PR]

Lin Jiu, Victor H. Moll, Christophe Vignat. A symbolic approach to some identities for Bernoulli-Barnes polynomials. International Journal of Number Theory, 2016, 12 (03), pp.649-662. ⟨10.1142/s1793042116500421⟩. ⟨hal-01294173⟩