Hi. I'm a bit stuck on this problem.

a) Find the partial fraction decomposition of

Let

After some working and expanding and simplifying i get the following:

b) Hence show that, ifis an entire function andthen

I can show this. Not hard. Just applying Cauchy's Integral Forumlae.

c) Calculate

So,

d) Calculate

Does this just equal tozerobecause one of the roots is outside |z|=2? Did I put it in correct termiology?