Divergent Series: Past, Present, Future …

C. R. Math. Rep. Acad. Sci. Canada Vol. 38 (3) 2016, pp. 85-98
(Received: 2015-02-11 , Revised: 2015-10-11)

Christiane RousseauDepartement de mathematiques et de statistique and CRM, Universite de Montreal, C.P. 6128, Succursale Centre-ville, Montreal, QC , H3C 3J7, Canada;
e-mail: rousseac@dms.umontreal.ca

Abstract/Résumé:

The paper presents some reflections of the author on divergent series and their role and place in mathematics over the centuries. The point of view presented here is limited to differential equations and dynamical systems.

L’article présente quelques réflexions de l’auteure sur les séries divergentes, et leur rôle et place en mathématiques au courant des siècles. Le point de vue présenté ici est limité aux équations différentielles et aux systèmes dynamiques.

Keywords: Borel summability, Divergent series, Euler dierential equation, Stokes phenomenon, resummation

AMS Subject Classification: Asymptotics; summation methods, Stokes phenomena and connection problems (linear and nonlinear) 34M30, 34M40

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