Find a general expression for the Laurent Series expansion of
$f(z) = (z-\alpha)^{-n}$
when $|z|>|\alpha|$.
I've tried expanding the function using the binomial theorem, and I've tried
integrating with the general formula for Laurent Series coefficients
using Cauchy's Integral formula, but I can't get the solution,
which I know is supposed to be
$\Sigma_{j=n}^{\infty} \alpha^{j-n} \frac{(j-1)!}{(n-1)!(j-n)!}z^{-j}$
Best Answer
$$(z-\alpha)^{-n} = \frac1{z^n} \left(1-\frac\alpha z\right)^{-n}.$$
Now expand the (...) term using the generalized binomial theorem.