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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- Jul 18th 2012, 01:32 PMjsauce59power 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

- Jul 18th 2012, 01:44 PMgirdavRe: power series and center of convergence
Write it as $\displaystyle \frac{-2a}{a^2-x^2}=\frac{-2}a\frac 1{1-\left(\frac xa\right)^2}$ in order to use the expansion of $\displaystyle \frac 1{1+t^2}$ in power series.