Periodica Mathematica Hungarica

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

Laurent expansion of an inverse of a function matrix

  • Cs. J. Hegedűs


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.


General Procedure Taylor Expansion Function Matrix Laurent Expansion Laurent Coefficient 
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  1. [1]
    J. L. Beeby, The density of electrons in a perfect or imperfect lattice,Proc. Roy. Soc. Ser. A 302 (1967), 113–136.Google Scholar
  2. [2]
    H. Bach, On the downhill method,Comm. ACM 12 (1969), 675–677.CrossRefGoogle Scholar
  3. [3]
    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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