Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

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

share|improve this question
add comment

1 Answer 1

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.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.