Multi-point Taylor expansions of analytic functions
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- by José L. López and Nico M. Temme PDF
- Trans. Amer. Math. Soc. 356 (2004), 4323-4342 Request permission
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.References
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Additional Information
- José L. López
- Affiliation: Departamento de Matématica e Informática, Universidad Pública de Navarra, 31006-Pamplona, Spain
- ORCID: 0000-0002-6050-9015
- Email: jl.lopez@unavarra.es
- Nico M. Temme
- Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
- Email: nicot@cwi.nl
- 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 - © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 4323-4342
- MSC (2000): Primary 30B10, 30E20; Secondary 40A30
- DOI: https://doi.org/10.1090/S0002-9947-04-03619-0
- MathSciNet review: 2067121