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Math Help - poles

  1. #1
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    poles

    let D\subset \mathbb{C} be open, let \to\mathbb{C}" alt="f\to\mathbb{C}" /> be holomorphic, and let z_0 \epsilon \mathbb{C}`D be a zero of order one of f. Show that
    res (\frac{1}{f};z_0)=\frac{1}{f'(z_0)}


    let D\subset \mathbb{C} be open, let \to\mathbb{C}" alt="f\to\mathbb{C}" /> be holomorphic, and let z_0 \epsilon \mathbb{C}`D be a simple pole for f. Show that
    res(gf;z_0)=g(z_0)res(f;z_0)
    for every holomorphic function \cup z_0 \to \mathbb{C}" alt="g\cup z_0 \to \mathbb{C}" />

    any tips?


    found it online
    http://books.google.ca/books?id=WZX4...sult#PPA175,M1
    don't know if that link works since it's rather convoluted, Complex analysis by serge lang page 175
    in case anyone else wanted to know this
    Last edited by jbpellerin; November 9th 2008 at 07:02 PM. Reason: found it myself :)
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