The coefficients of the Laurent series expansions of real analytic functions |
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Authors: | Alexander Abian James A Wilson |
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Institution: | 1. Department of Mathematics, Iowa State University, 50011, Ames, Iowa, USA
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Abstract: | Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated. |
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