From Divergent Power Series to Analytic Functions: Theory and Application of Multisummable Power Series (Lecture Notes in Mathematics, 1582)

Balser, Werner

ISBN 10: 3540582681 / ISBN 13: 9783540582687

Editore: Springer, 1994

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Titolo: From Divergent Power Series to Analytic ...

Casa editrice: Springer

Data di pubblicazione: 1994

Legatura: paperback

Condizione: New

Descrizione articolo

Riassunto:

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.

Contenuti:

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.