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MARC 21

Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations
Tag	Description
020	$a9780387225982
082	$a515
099	$aOnline resource: Springer
100	$aBalser, Werner$d1946-
245	$aFormal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations$h[EBook]$cby Werner Balser.
260	$aNew York, NY$bSpringer$c2000.
300	$aXVIII, 301 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aUniversitext
505	$aBasic 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 -- Stokes’ Phenomenon -- Multisummable Power Series -- Ecalle’s Acceleration Operators -- Other Related Questions -- Applications in Other Areas, and Computer Algebra -- Some Historical Remarks.
520	$aSimple 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aUniversitext
856	$uhttp://dx.doi.org/10.1007/b97608