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Archive for History of Exact Sciences

, Volume 61, Issue 5, pp 519–535 | Cite as

A new look at E.G. Björling and the Cauchy sum theorem

  • Kajsa BråtingEmail author
Article

Abstract

We give a new account of Björling’s contribution to uniform convergence in connection with Cauchy’s theorem on the continuity of an infinite series. Moreover, we give a complete translation from Swedish into English of Björling’s 1846 proof of the theorem. Our intention is also to discuss Björling’s convergence conditions in view of Grattan-Guinness’ distinction between history and heritage. In connection to Björling’s convergence theory we discuss the interpretation of Cauchy’s infinitesimals.

Keywords

Uniform Convergence Function Concept Pointwise Convergence Convergence Theory Nonstandard Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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