Author | Balser, Werner. author |
---|---|

Title | From Divergent Power Series to Analytic Functions [electronic resource] : Theory and Application of Multisummable Power Series / by Werner Balser |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1994 |

Connect to | http://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