Identities for Bernoulli polynomials related to multiple Tornheim zeta functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:476

Article

Dilcher, Karl¹  Straub, Armin²  Vignat, Christophe^3,4 

[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 4R2, Canada

[2] Univ S Alabama, Dept Math & Stat, Mobile, AL 36688 USA

[3] Univ Paris Sud, LSS Supelec, Orsay, France

[4] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

关键词: Bernoulli polynomials;    Bernoulli numbers;    Eulerian polynomials;    Convolution identities;   

DOI  :  10.1016/j.jmaa.2019.03.071

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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