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Identities for Bernoulli polynomials related to multiple Tornheim zeta functions

Identities for Bernoulli polynomials related to multiple Tornheim zeta functions
Karl Dilcher, Armin Straub, Christophe VignatJournal of Mathematical Analysis and Applications — Volume 476, Number 2, 2019, Pages 569-584

Abstract

We show that each member of a doubly infinite sequence of highly nonlinear expressions of Bernoulli polynomials, which can be seen as linear combinations of certain higher-order convolutions, is a multiple of a specific product of linear factors. The special case of Bernoulli numbers has important applications in the study of multiple Tornheim zeta functions. The proof of the main result relies on properties of Eulerian polynomials and higher-order Bernoulli polynomials.

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BibTeX

@article{bernoulli-zeta-2019,
    author = {Karl Dilcher and Armin Straub and Christophe Vignat},
    title = {Identities for Bernoulli polynomials related to multiple Tornheim zeta functions},
    journal = {Journal of Mathematical Analysis and Applications},
    year = {2019},
    volume = {476},
    number = {2},
    pages = {569--584},
    doi = {10.1016/j.jmaa.2019.03.071},
}