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From Divergent Power Series to Analytic Functions

Theory and Application of Multisummable Power Series

  • Book
  • © 1994

Overview

Authors:
  1. Werner Balser
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1582)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Asymptotic power series

    • Werner Balser
    Pages 1-12

  3. Laplace and borel transforms

    • Werner Balser
    Pages 13-22

  4. Summable power series

    • Werner Balser
    Pages 23-32

  5. Cauchy-Heine transform

    • Werner Balser
    Pages 33-40

  6. Acceleration operators

    • Werner Balser
    Pages 41-52

  7. Multisummable power series

    • Werner Balser
    Pages 53-74

  8. Some equivalent definitions of multisummability

    • Werner Balser
    Pages 75-81

  9. Formal solutions to non-linear ODE

    • Werner Balser
    Pages 83-101

  10. Back Matter

    Pages 103-110
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Keywords

About this book

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.

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