Calculating Residium of Complex Integral |z|=1

[nhrock3]

$$\int_{|z|=1}^{nothing } \frac{1}{z}e^{\frac{1}{z}}$$
in this integral there is no upper bound
its around |z|=1

there are no poles here
only singular significant
what to do here
when calclating the residium
??

 

[Char. Limit]

I believe, and don't trust me on this, that it's asking you to calculate a path integral around the unit circle on the complex plane. There's no "upper bound" because the integral is describing a path, not just a starting point and an ending point. Incidentally, I believe that starting and ending points are the same.

 

[hunt_mat]

Start by expanding $$\exp (1/z)$$ as a power series, multiply by 1/z and look for the z^{-1} term. That will be your residue.

Mat

 

[Mute]

A change of variables $w = 1/z$ will also do the trick.