Multi-point Taylor Expansions of Analytic Functions
نویسندگان
چکیده
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 TaylorLaurent expansions.
منابع مشابه
Modelling, Analysis and Simulation Modelling, Analysis and Simulation Multi-point Taylor expansions of analytic functions
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 Lau...
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