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Prove g(z) = 1/(2*pi*i) int_c f(s)ds/(s-z) is analytic? How can I with an integral?

  1. Apr 22, 2007 #1
    1. The problem statement, all variables and given/known data

    My text book has this question

    f is continuous on C which is a simple closed contour...

    Prove g(z) = 1/(2*pi*i) int_c f(s)ds/(s-z) is analytic?

    I understand that you use Cauchy-Riemann proof for analytic functions, but how do I find the derivatve of a function that has an integral inside of it? Any suggestions?

    2. Relevant equations

    I thought maybe somehow I'd have to use the Cauchy Integral formula, but what version of it should I use? and should I even use that - the only reason I think that is that is the question in the text book after the Cauchy Integral topic! :)

    3. The attempt at a solution

    I'm not sure where to start because I dont know how to differentiate the funciton because of the integral there and not sure how to get rid of it! :yuck:
  2. jcsd
  3. Apr 22, 2007 #2


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    Is that exactly how the question is stated? Does it say that f is continuous on C, or does it say f is analytic on and inside C?
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