Laurent series for integration

Hey,

Just going over past papers and I think I did this question alright, just wanted to double check.

The question is

http://img443.imageshack.us/img443/83/56521555.jpg

so what I did was:

Sorry there are a few bugs in my tex, c1/... is supposed to be a frac, I couldnt see why it wasnt making it a frac, the first sum is supposed to be to infinity not y, it says infinity in the code haha, and theres afew smaller ones.

With Cauchy

I think it might be ok, I'm just unsure about my cauchy integral, is it fine what i did? The reason im unsure is that cauchys formula doesnt have a z squared it just has a z, but I couldnt really find a way to get around it, I guess the more correct way would be to use the cauchy derivative formula. <- just ran through it quicky and got g'(0) = 1 and then the integral was = 2iPi

Thanks in advance (Talking)