Multi-point Taylor Expansions of Analytic Functions
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
Abstract
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in several points as well as Taylor-Laurent expansions.
Keywords
Cite
@article{arxiv.math/0410436,
title = {Multi-point Taylor Expansions of Analytic Functions},
author = {José L. López and Nico M. Temme},
journal= {arXiv preprint arXiv:math/0410436},
year = {2007}
}
Comments
20 pages, 7 figures. Keywords: multi-point Taylor expansions, Cauchy's theorem, analytic functions, multi-point Laurent expansions, uniform asymptotic expansions of integrals