A symbolic approach to some identities for Bernoulli–Barnes polynomials
2016 ◽
Vol 12
(03)
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pp. 649-662
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Keyword(s):
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.
2017 ◽