http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
From divergent power series to analytic functions
theory and application of multisummable power series
1 online resource (x, 106 pages) : illustrations.
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.
1. Asymptotic Power Series -- 2. Laplace and Borel Transforms -- 3. Summable Power Series -- 4. Cauchy-Heine Transform -- 5. Acceleration Operators -- 6. Multisummable Power Series -- 7. Some Equivalent Definitions of Multisummability -- 8. Formal Solutions to Non-Linear ODE.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
Includes bibliographical references (pages [103]-106) and index.
Berlin ; New York : Springer-Verlag, ©1994
Lecture notes in mathematics (Springer-Verlag) ; 1582