# Residue of a function

Hi. I'm trying to find the residue of

$$\exp{\frac{1}{z}}$$

at z=0 since it is a pole, so I can integrate the function over the unit circle counterclockwise. I expanded this function in Laurent Series to get

$$\exp{\frac{1}{z}} = 1 + \frac{1}{1!z} + \frac{1}{2!z^2}+ ...$$

So in this case the residue is the coefficient of 1/z which is 1. Is this method correct? There is no answer to it in the book...

EDIT: If you guys can find the residue using another method, please teach me.
EDIT 2: Fixed the typo :p

Last edited:

marcusl
Gold Member
Perfect, except you need z^(-2) in the 3rd term above (i'm sure you made a typo).

Oh yes it is a typo. Thanks for the input.

HallsofIvy