José L. López, Nico M. Temme
Published 2004-10-20Version 1
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.
Comments: 20 pages, 7 figures. Keywords: multi-point Taylor expansions, Cauchy's theorem, analytic functions, multi-point Laurent expansions, uniform asymptotic expansions of integrals
Journal: Trans. Amer. Math. Soc. 356, 4323--4342, 2004
Two-point Taylor Expansions of Analytic Functions
A new family of analytic functions defined by means of Rodrigues type formula
Self-referential Functions
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