Multi-point Taylor Expansions of Analytic Functions

Details Multi-point Taylor Expansions of Analytic Functions Multi-point Taylor Expansions of Analytic Functions

2004-10-20

arxiv.org/abs/math/0410436v1

Trans. Amer. Math. Soc. 356, 4323--4342, 2004

Mathematics

Classical Analysis and ODEs

20 pages, 7 figures. Keywords: multi-point Taylor expansions, Cauchy's theorem, analytic functions, multi-point Laurent expans

Scientific paper

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.

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