(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the coefficients [itex]c_n[/itex] of the Laurent series expansion

[itex]\frac{1}{(z-1)^2} = \sum_{n = -\infty}^{\infty} c_n z^n[/itex]

that is valid for [itex]|z| > 1[/itex].

2. Relevant equations

none

3. The attempt at a solution

I found expansions valid for [itex]|z|>1[/itex] and [itex]|z|<1[/itex]:

[itex]\sum_{n = 0}^{\infty} \left(n-1\right)z^n, |z|>1[/itex] and

[itex]\sum_{n = 2}^{\infty} \left(n-1\right)z^{-n}, |z|<1[/itex]

I know that if I negate the n's in the second equation and change the index of the sum to go from -∞ to -2 I can add them together to get the sum from -∞ to ∞, but I don't know what to do about the missing n=1 term. Any suggestions?

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# Homework Help: Laurent Series Expansion coefficient for f(z) = 1/(z-1)^2

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