Abstract
In this chapter we define the notion of asymptotic expansions, in particular Gevrey asymptotics, and we show their main properties. To do so, it will be notationally convenient to restrict ourselves to power series in z, hence statements on asymptotic behavior of functions are always made for the variable z tending to the origin in some region. The main applications will be to formal analytic or meromorphic transformations, i.e., series in 1/z, but we trust that the reader will be able to make the necessary reformulation of the results.
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© 2000 Springer-Verlag New York, Inc.
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(2000). Asymptotic Power Series. In: Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations. Universitext. Springer, New York, NY. https://doi.org/10.1007/0-387-22598-6_4
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DOI: https://doi.org/10.1007/0-387-22598-6_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98690-6
Online ISBN: 978-0-387-22598-2
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