série divergente; convergence au sens de Cesaro ou d'Abel; sommation par prolongement analytique; sommation lisse; dialectique hégélienne
Abstract :
[fr] La série de Grandi, dont les termes sont alternativement égaux à 1 et à -1, est une série divergente emblématique. Nous donnons son histoire qui nous paraît conforme à la dialectique hégélienne. Nous en déduisons quelques constatations générales relatives à l'évolution temporelle de concepts mathématiques, ainsi qu'à la nature surprenante de certains résultats obtenus par des mathématiciens célèbres.
Disciplines :
Mathematics
Author, co-author :
Bair, Jacques ; Université de Liège > HEC Liège > HEC Liège
Language :
French
Title :
A propos de la série de Grandi
Publication date :
December 2015
Journal title :
Losanges
ISSN :
2032-0264
eISSN :
2593-0443
Publisher :
Société Belge des Professeurs de Mathématiques d'Expression Française (SBPMef), Mons, Belgium
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