From divergent power series to analytic functions : theory and application of multisummable power series
Author(s)
Bibliographic Information
From divergent power series to analytic functions : theory and application of multisummable power series
（Lecture notes in mathematics, 1582）
Springer-Verlag, c1994
- : gw
- : us
Available at / 91 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: gwL/N||LNM||1582RM941015
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: gwdc20:515.2432/b2162070308890
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Note
Includes bibliographical references (p. [103]-106), index and list of symbols
Description and Table of Contents
Description
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.
Table of Contents
Asymptotic power series.- Laplace and borel transforms.- Summable power series.- Cauchy-Heine transform.- Acceleration operators.- Multisummable power series.- Some equivalent definitions of multisummability.- Formal solutions to non-linear ODE.
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