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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

$\Sigma_{j=n}^{\infty} \alpha^{j-n} \frac{(j-1)!}{(n-1)!(j-n)!}z^{-j}$

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up vote 2 down vote accepted

$$(z-\alpha)^{-n} = \frac1{z^n} \left(1-\frac\alpha z\right)^{-n}.$$

Now expand the (...) term using the generalized binomial theorem.

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