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＜E-Book＞
From Divergent Power Series to Analytic Functions : Theory and Application of Multisummable Power Series / by Werner Balser
(Lecture Notes in Mathematics. ISSN:16179692 ; 1582)

Edition	1st ed. 1994.
Publisher	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Year	1994
Size	X, 114 p : online resource
Authors	*Balser, Werner author SpringerLink (Online service)
Subjects	LCSH:Functions of complex variables LCSH:Mathematical analysis LCSH:Mathematical physics FREE:Functions of a Complex Variable FREE:Analysis FREE:Theoretical, Mathematical and Computational Physics
Notes	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 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 HTTP:URL=https://doi.org/10.1007/BFb0073564

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