TY  - BOOK
AU  - Balser,Werner
ED  - SpringerLink (Online service)
TI  - From Divergent Power Series to Analytic Functions: Theory and Application of Multisummable Power Series 
T2  - Lecture Notes in Mathematics,
SN  - 9783540485940
AV  - QA299.6-433 
U1  - 515 23
PY  - 1994///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Mathematical physics
KW  - Analysis
KW  - Mathematical and Computational Physics
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0073564
ER  -