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?
What is the Laurent Series of $\cos{\frac{1}{\sqrt{z}}}$ at point $z=0$?
1
$\begingroup$
complex-analysis
1 Answers
2
$\begin{align} \cos z = \sum_{n=0}^\infty \frac{(-1)^n z^{2n}}{(2n)!} \\ \cos \frac{1}{\sqrt{z}} = \sum_{n=0}^\infty \frac{(-1)^n z^{-n}}{(2n)!} \end{align}$ what's wrong with that?