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If $f$ is holomorphic on $0<|z|<2$ and satisfies $ f(\frac{1}{n}) = n^2 $ and $ f(-\frac{1}{n}) = n^3 $ what kind of singularity does f have at 0?

Well at least is not removable since it's not bounded. But I don't know how to continue.

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If $f$ had a pole of order $k$, it would have asymptotics like $f(z)\sim \mathrm{const}\cdot z^{-k}$ as $z$ approaches zero in any way. –  Alexander Shamov Nov 3 '12 at 18:06
    
Thanks! you are right xd –  Daniel Nov 3 '12 at 21:59
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