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arXiv · 1402.2993

Generalized Bernoulli numbers and a formula of Lucas

V. H. Moll·C. Vignat
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Abstract

An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The value of this sum is then given in terms of the Meixner-Pollaczek polynomials.

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V. H. Moll, C. Vignat. 2014-02-12. Generalized Bernoulli numbers and a formula of Lucas. https://arxiv.org/abs/1402.2993

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