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Math Help - series expansion

  1. #1
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    series expansion

    how would i write f(z)=\frac {(z^2 -1)^ {1 \over 2}}{z^2 + 1} as a series expansion?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by bigdoggy View Post
    how would i write f(z)=\frac {(z^2 -1)^ {1 \over 2}}{z^2 + 1} as a series expansion?
    \frac{1}{1+z^2}=1-(z^2)+(z^2)^2-(z^2)^3+...

    so

    f(z)=\frac{(z^2 -1)^{1/2}}{z^2 + 1}=\sqrt{z^2-1}\bigg(1-z^2+z^4-z^6+...\bigg)

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  3. #3
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    thanks. i'm trying to find the value of the integral of that function around a circle of large radius. The function is complex and has a branch cut in the section [-1,1] of the real axis.
    So I need to figure out how to express that function as a series expansion to begin with...
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