Identities for Bernoulli polynomials related to multiple Tornheim zeta functions

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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https://hal.archives-ouvertes.fr/hal-02146468
Contributor : Christophe Vignat <>
Submitted on : Tuesday, June 4, 2019 - 6:21:28 AM
Last modification on : Monday, July 8, 2019 - 11:38:01 AM

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Karl Dilcher, Armin Straub, Christophe Vignat. Identities for Bernoulli polynomials related to multiple Tornheim zeta functions. Australian Journal of Mathematical Analysis and Applications, Austral Internet Publishing, 2019, 476 (2), pp.569-584. ⟨10.1016/j.jmaa.2019.03.071⟩. ⟨hal-02146468⟩

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