A new look at E.G. Björling and the Cauchy sum theorem |
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Authors: | Kajsa Bråting |
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Affiliation: | (1) Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden |
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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. |
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