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AuthorBalser, Werner. author
TitleFrom Divergent Power Series to Analytic Functions [electronic resource] : Theory and Application of Multisummable Power Series / by Werner Balser
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1994
Connect tohttp://dx.doi.org/10.1007/BFb0073564
Descript X, 114 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Functions of complex variables Physics Mathematics Functions of a Complex Variable Analysis Theoretical Mathematical and Computational Physics



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