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kpizzano
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Homework Statement
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].
Homework Equations
none
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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