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From divergent power series to analytic functions : theory and application of multisummable power series /

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Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact t...

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Bibliographic Details
Main Author: Balser, Werner, 1946-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer-Verlag, [1994]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1582.
Subjects:
Power series.
Asymptotic expansions.
Summability theory.
Analytic functions.
Séries de puissances.
Développements asymptotiques.
Sommabilité.
Fonctions analytiques.
Reeksontwikkelingen.
Asymptotisch gedrag.
Analytische Funktion.
Potenzreihe.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Asymptotic Power Series
  • 2. Laplace and Borel Transforms
  • 3. Summable Power Series
  • 4. Cauchy-Heine Transform
  • 5. Acceleration Operators
  • 6. Multisummable Power Series
  • 7. Some Equivalent Definitions of Multisummability
  • 8. Formal Solutions to Non-Linear ODE.