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Math Help - Laurent Series

  1. #1
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    Laurent Series

    Find the Laurent series representation of \frac{e^z}{(z+1)^2} for (0<\left |z+1 \right |< \infty).

    I really don't understand the process of getting the series representation.
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  2. #2
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    Quote Originally Posted by davesface View Post
    Find the Laurent series representation of \frac{e^z}{(z+1)^2} for (0<\left |z+1 \right |< \infty).

    I really don't understand the process of getting the series representation.
    First get the Taylor's series for e^z about the point z= -1. Can you do that?
    (The Taylor's series for f(z) about z= a is \sum_{n=0}^\infty \frac{f^{(n)}(a)}{a!}(z- a)^n where f^{(n)} indicates the nth derivative. It should be easy to find the nth derivative of e^z at z= -1.

    Then divide each term by (z+ 1)^2
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    Taking that approach, I get L(f(z))=\frac{1}{(z+1)^2e}*\sum_{n=0}^{\infty}\fra  c{(z+1)^n}{(-1)!}. Shouldn't it be n! instead of a!?
    Last edited by davesface; April 22nd 2010 at 10:40 AM.
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