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find the laurent series centered at $z=0$ for the rational functions below. Determine the largest open set in $C$ for which each series converges
$$\frac{1}{(z^2-1)(z^2-4)}.$$

I have no idea how to do this.

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    \frac{1}{((z^2)-1)((z^2)-4)}2012-12-12
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    Actually try going by the route given here: http://en.wikipedia.org/wiki/Laurent_series. Try doing some integrations, put some work in it. Tell us where the problem exactly lies, based on yourndifficulties.2012-12-12
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    Perhaps you can decompose the rational function by partial fractions, and then rewrite each term as a Laurent series about $z=0$. Then combine everything.2012-12-12
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    **Hint:** 1. Where singularities of the function $\dfrac{1}{(z^2-1)(z^2-4)}$ are located? What is the type of these singularities? 2. Try decomposition of rational function $\dfrac{1}{(z^2-1)(z^2-4)}$ by partial fractions2012-12-12

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