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arXiv.org e-Print Archive
Preprint . 2014
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Article . 2015
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The Fibonacci Quarterly
Article . 2015 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2014
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Generalized Bernoulli Numbers and a Formula of Lucas

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2015Embargo end date: 01 Jan 2014 English Publisher:Informa UK LimitedJournal:The Fibonacci Quarterly, volume 53, pages 349-359 (issn: 0015-0517, eissn: 2641-340X, Copyright policy )
Authors: Moll, Victor H.; Vignat, Christophe;

doi: 10.1080/00150517.2015.12428254 , 10.48550/arxiv.1402.2993

arXiv: http://arxiv.org/abs/1402.2993

Generalized Bernoulli Numbers and a Formula of Lucas

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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Keywords

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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