So what I did was $\frac{1}{z^2}\frac{1}{z^2+1} = \frac{1}{z^2}\frac{1}{z^2}\frac{1}{1+\frac{1}{z^2}} = \frac{1}{z^4}\sum \frac{(-1)^n}{z^{2n}} = \sum z^{-2n-4}(-1)^n$ and I need to know if this is correct.
2026-03-29 11:20:03.1774783203
Laurent series for $\frac{1}{z^2(z^2+1)}$
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If you are looking for the Laurentseries centered at 0,your computations are correct.
fred