I must find the Laurent series for $f(z) = \frac{e^z}{z^2}$ in powers of $z$ for the annulus $ |z| > 0$.
I wrote $f(z) = \frac{1}{z^2} \sum_{n=0}^{\infty} \frac{z^n}{n!} = \sum_{n=0}^{\infty} \frac{z^{n-2}}{n!} = \sum_{n=-2}^{\infty} \frac{z^{n}}{(n+2)!} $
Is this correct? I didn't apply the annulus being $z > 0$ anywhere, I believe that the Taylor expansion for $e^z$ can be applied for all values of $z$ in the complex plane.