umu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Explaining Kummer's test
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Mathematical theorems and their proofs are often described as being beautyful, natural or explanatory. This paper treats the last case  and discusses explanatory versus non explanatory proofs using  a convergence theorem for positive series due to Kummer, called Kummer's test. This example was studied by Pringsheim already in the beginning in the last century and has recently been discussed by Hafner and Mancuso in relation to Steiner's criteria for an explanatory proof. We provide a mathematical analysis of Kummer's test and give a proof that we claim is explanatory in this sense. Besides this we answer a number of questions that are frequently asked about the test.

Place, publisher, year, edition, pages
2015.
Keyword [en]
Positive series, convergence, convergence test, Kummer's test, explanatory proof
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-104407OAI: oai:DiVA.org:umu-104407DiVA: diva2:819461
Available from: 2015-06-10 Created: 2015-06-10 Last updated: 2015-07-01Bibliographically approved

Open Access in DiVA

fulltext(104 kB)1321 downloads
File information
File name FULLTEXT01.pdfFile size 104 kBChecksum SHA-512
4ab0b787dd506b423174b47e6a0add3636d2460fbd2c19d5b0048ad05a84004ce15a1e19d4bef9732a11a8b25c4dd55c82269a259b03cf166d82c2c6341a2858
Type fulltextMimetype application/pdf

Authority records BETA

Sjödin, Tord

Search in DiVA

By author/editor
Sjödin, Tord
By organisation
Department of Mathematics and Mathematical Statistics
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 1321 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 138 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf