Laurent Series and the Residue Theorem

  • John M. Howie
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


In Section 3.5 we looked briefly at functions with isolated singularities. It is clear that a function f with an isolated singularity at a point c cannot have a Taylor series centred on c. What it does have is a Laurent1 series, a generalized version of a Taylor series in which there are negative as well as positive powers of zc.


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  1. 1.
    Pierre Alphonse Laurent, 1813–1854.Google Scholar
  2. 2.
    Felice Casorati, 1835–1890.Google Scholar

Copyright information

© Springer-Verlag London 2003

Authors and Affiliations

  • John M. Howie
    • 1
  1. 1.School of Mathematics and Statistics, Mathematical InstituteUniversity of St AndrewsNorth Haugh, St Andrews, FifeUK

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