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Periodica Mathematica Hungarica

, Volume 6, Issue 1, pp 75–86 | Cite as

Laurent expansion of an inverse of a function matrix

  • Cs. J. Hegedűs
Article

Abstract

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.

Keywords

General Procedure Taylor Expansion Function Matrix Laurent Expansion Laurent Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    J. L. Beeby, The density of electrons in a perfect or imperfect lattice,Proc. Roy. Soc. Ser. A 302 (1967), 113–136.Google Scholar
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    H. Bach, On the downhill method,Comm. ACM 12 (1969), 675–677.CrossRefGoogle Scholar
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    E. Bodewig,Matrix Calculus, North-Holland Publishing Co., Amsterdam, 1959.Google Scholar
  4. [4]
    G. Sansone andJ. Gerretsen,Lectures on the Theory of Functions of a Complex Variable, Vol. 1 Noordhoff, Groningen, 1960.Google Scholar

Copyright information

© Akadémiai Kiadó 1975

Authors and Affiliations

  • Cs. J. Hegedűs
    • 1
  1. 1.MTA Központi Fizikai Kutató IntézeteBudapestHungary

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