From Divergent Power Series to Analytic Functions

Theory and Application of Multisummable Power Series
1. Auflage 1994
ISBN: 978-3-540-58268-7
Verlag: Springer

Buch, Englisch, Band 1582, 114 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 454 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Balser, Werner

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.