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From Divergent Power Series to Analytic Functions [electronic resource] : Theory and Application of Multisummable Power Series / by Werner Balser.

Author/Creator:
Balser, Werner. author., Author,
Publication:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994.
Format/Description:
Book
1 online resource (X, 114 pages)
Series:
Lecture Notes in Mathematics, 0075-8434 ; 1582
Lecture Notes in Mathematics, 0075-8434 ; 1582
Contained In:
Springer eBooks
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Details

Subjects:
Functions of complex variables.
Global analysis (Mathematics).
Local subjects:
Functions of a Complex Variable. (search)
Analysis. (search)
Theoretical, Mathematical and Computational Physics. (search)
System Details:
text file PDF
Summary:
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.
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.
Contributor:
SpringerLink (Online service)
Other format:
Printed edition:
Printed edition:
ISBN:
9783540485940
Publisher Number:
10.1007/BFb0073564 doi
Access Restriction:
Restricted for use by site license.