Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

• Main Author: Balser, Werner (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2000.
• Series: Universitext
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Analysis.

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 comput...

Table of Contents:

• 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
• Stokes’ Phenomenon
• Multisummable Power Series
• Ecalle’s Acceleration Operators
• Other Related Questions
• Applications in Other Areas, and Computer Algebra
• Some Historical Remarks.