From Divergent Power Series to Analytic Functions: Theory and Application of Multisummable Power Series

Werner Balser (auth.)3540582681, 9783540582687

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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Table of contents :
Asymptotic power series….Pages 1-12
Laplace and borel transforms….Pages 13-22
Summable power series….Pages 23-32
Cauchy-Heine transform….Pages 33-40
Acceleration operators….Pages 41-52
Multisummable power series….Pages 53-74
Some equivalent definitions of multisummability….Pages 75-81
Formal solutions to non-linear ODE….Pages 83-101