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The function $\cos{\frac{1}{\sqrt{z}}}$ is analytic at any neighborhood of $z=0$, but I find it hard to get the Laurent Series of the function. Any help?

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up vote 2 down vote accepted

$$\begin{align} \cos z = \sum_{n=0}^\infty \frac{(-1)^n z^{2n}}{(2n)!} \\ \cos \frac{1}{\sqrt{z}} = \sum_{n=0}^\infty \frac{(-1)^n z^{-n}}{(2n)!} \end{align}$$ what's wrong with that?

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