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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Multi-point Taylor expansions of analytic functions


Authors: José L. López and Nico M. Temme
Journal: Trans. Amer. Math. Soc. 356 (2004), 4323-4342
MSC (2000): Primary 30B10, 30E20; Secondary 40A30
Published electronically: May 28, 2004
MathSciNet review: 2067121
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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.


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Additional Information

José L. López
Affiliation: Departamento de Matématica e Informática, Universidad Pública de Navarra, 31006-Pamplona, Spain
Email: jl.lopez@unavarra.es

Nico M. Temme
Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Email: nicot@cwi.nl

DOI: https://doi.org/10.1090/S0002-9947-04-03619-0
Keywords: Multi-point Taylor expansions, Cauchy's theorem, analytic functions, multi-point Laurent expansions, uniform asymptotic expansions of integrals
Received by editor(s): November 14, 2002
Published electronically: May 28, 2004
Additional Notes: The first author thanks the saving bank Caja Rural de Navarra for its financial support. He also acknowledges the scientific and financial support of CWI in Amsterdam
The authors thank the referee for the comments on the first version of the paper
Article copyright: © Copyright 2004 American Mathematical Society