Some Consequences of Cauchy’s Theorem

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


We have already observed in Theorem 5.13 that if σ is a circle with centre 0 then
$$ \int_\sigma {\frac{1}{z}} dz = 2\pi i $$


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  1. 1.
    Siméon Denis Poisson, 1781–1840.Google Scholar
  2. 2.
    Joseph Liouville, 1809–1882.Google Scholar
  3. 3.
    Johann Carl Friedrich Gauss, 1777–1855.Google Scholar
  4. 4.
    Brook Taylor, 1685–1731.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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