Laurent expansion of an inverse of a function matrix
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This paper suggests a general procedure based on the Taylor expansion of a function matrixF(z) for calculating the Laurent expansion ofF−1(z) around an isolated pole. It is shown that in order to compute thejth Laurent coefficient matrixBj ofF−1(z), one needs in any case the Taylor coefficientsA0, A1,..., A2n+j ofF(z), wheren is the order of the pole.
Theorem 1 helps to determine the order of the pole, while Theorem 2 shows also how the Laurent coefficients can be computed in the general case.
KeywordsGeneral Procedure Taylor Expansion Function Matrix Laurent Expansion Laurent Coefficient
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