use the Cauchy residue theorem show that for any integer ,

where is a circle of radius unity centred at

this part was easy enough.

(by Cauchy residue theorem)

if not 0, or if

now i have to use this result to deduce that, if you are given

then

and

where is the derivative of with respect to z

i have no idea how to even start the second part of this question!! any tips??