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I Complex Analysis, holomorphic in circle.

  1. Jul 23, 2016 #1
    Hi, I have a question regarding corollary 2.3. in the uploaded image.

    it looks very trivial to me becauese Cauchy's theorem states "if f(z) is holomorphic, its closed loop integral
    will be always 0". Is this what the author is trying to say? whats the necesseity of the larger disk D' at here?
    Why do we use D'?
     

    Attached Files:

  2. jcsd
  3. Jul 23, 2016 #2
    You understand right, just do not bother about that. Usually such a type argument (about D') is already contained in the proof of the Cauchy theorem. Look above how they formulate Cauchy theorem.

    the loop must be in the domain where f is holomorphic and this loop must be shrinkable in this domain. and the loop must be contained compactly in the domain
     
    Last edited: Jul 23, 2016
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