## From Divergent Power Series to Analytic Functions: Theory and Application of Multisummable Power SeriesMultisummability 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. |

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### Contents

Asymptotic Power Series | 1 |

Laplace and Borel Transforms | 13 |

Summable Power Series | 23 |

Copyright | |

6 other sections not shown

### Other editions - View all

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### Common terms and phrases

admissible admissible index tupel admissible with respect algebra analytic analytically continued application arbitrary assume assumptions asymptotic expansion bisecting direction boundary bounded called Chapter choose closed subsector complex conclude consider converges corresponding covering define definition denote depending easily equal equivalent estimate Exercises exists exponential exponential size finite fixed formal power series formal solution function Gevrey given gives hence holds implies independent infinite radius integral k-summable in direction larger Lemma linear Moreover multisummability observe obtain opening operator origin osism path positive power series expansion problem Proof properties Proposition prove regions Remark resp result Riemann surface Section sector sector of infinite seen sequence singular directions sufficiently large sufficiently small suitable summability Theorem Theory unique variables write zero