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Mathematics Magazine
Article
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arXiv.org e-Print Archive
Preprint . 2018
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Mathematics Magazine
Article . 2012 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2018
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https://dx.doi.org/10.4169/mat...
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Close Encounters with the Stirling Numbers of the Second Kind

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2012Embargo end date: 01 Jan 2018 English Publisher:Informa UK LimitedJournal:Mathematics Magazine, volume 85, pages 252-266 (issn: 0025-570X, eissn: 1930-0980, Copyright policy )
Authors: Boyadzhiev, Khristo N.;

doi: 10.4169/math.mag.85.4.252 , 10.48550/arxiv.1806.09468

arXiv: 1806.09468

Close Encounters with the Stirling Numbers of the Second Kind

Abstract

This is a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis. We tell the story of their birth in the book of James Stirling (1730) and show how they mature in the works of Johann Grunert (1843). We demonstrate their usefulness in several differentiation formulas. The reader can also see the connection to Bernoulli numbers, to Euler polynomials and to power sums.

19 pages. This is a modified version of the paper published in the Math Magazine (2012)

Related Organizations
Keywords

Mathematics - History and Overview, History and Overview (math.HO), FOS: Mathematics, 11B83, 05A19

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    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).
    		 64
    popularity
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    		 Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
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!
64
Top 1%
Top 1%
Average
Green
bronze