Author	Balser, Werner. author
Title	Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations [electronic resource] / by Werner Balser
Imprint	New York, NY : Springer New York, 2000
Connect to	http://dx.doi.org/10.1007/b97608
Descript	XVIII, 301 p. online resource

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series

Basic Properties of Solutions -- Singularities of First Kind -- Highest-Level Formal Solutions -- Asymptotic Power Series -- Integral Operators -- Summable Power Series -- Cauchy-Heine Transform -- Solutions of Highest Level -- Stokesโ Phenomenon -- Multisummable Power Series -- Ecalleโs Acceleration Operators -- Other Related Questions -- Applications in Other Areas, and Computer Algebra -- Some Historical Remarks

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Mathematics
5. Analysis