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Math Help - power series and center of convergence

  1. #1
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    power series and center of convergence

    I have a function g(x)=(2a)/(x^2-a^2) where a is some number greater than zero. I need to find a power series with a center of convergence at zero and then find the radius and the interval of convergence. Any help would be appreciated. Thanks
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  2. #2
    Super Member girdav's Avatar
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    Re: power series and center of convergence

    Write it as \frac{-2a}{a^2-x^2}=\frac{-2}a\frac 1{1-\left(\frac xa\right)^2} in order to use the expansion of \frac 1{1+t^2} in power series.
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