From divergent power series to analytic functions
Subtitle: theory and application of multisummable power series
By: Werner Balser.
Series: Lecture notes in mathematics ;; 1582; Lecture notes in mathematics (Springer-Verlag) ;; 1582.
Publisher: Springer-Verlag
Published: 1994
Place of publication: Berlin; New York
Language: eng
Number of pages: 106
Subjects: Power series.; Asymptotic expansions.; Summability theory.; Analytic functions.
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.
Notes: Includes bibliographical references (p. [103]-106) and index.