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From Divergent Power Series to Analytic Functions

Theory and Application of Multisummable Power Series

  • Authors
  • Werner Balser

Part of the Lecture Notes in Mathematics book series (LNM, volume 1582)

Table of contents

  1. Front Matter
    Pages I-X
  2. Werner Balser
    Pages 1-12
  3. Werner Balser
    Pages 13-22
  4. Werner Balser
    Pages 23-32
  5. Werner Balser
    Pages 33-40
  6. Werner Balser
    Pages 41-52
  7. Werner Balser
    Pages 53-74
  8. Werner Balser
    Pages 83-101
  9. Back Matter
    Pages 103-110

About this book

Introduction

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 that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

Keywords

Analytic Functions Divergent Power Series Formal power series Laplace transfomation Meromorphic function analytic function asymptotic expansions multisummability non-linear ODE

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073564
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58268-7
  • Online ISBN 978-3-540-48594-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site