How to calculate the Laurent series expansion of 1/(1-z)² in the region 1<|z|?

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SUMMARY

The discussion focuses on calculating the Laurent series expansion of the function 1/(1-z)² in the region where |z| > 1. A user expresses uncertainty about their informal method of polynomial division and seeks confirmation and proof of their results. It is noted that if a function is analytic on a domain, its Laurent series and Taylor series are identical, prompting a request for guidance on performing the Taylor series expansion for this function.

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Eldonbetan
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1. I am trying to calculate the laurent series expansion of the function 1/(1-z)² in the region 1<|z|


2. None


3. I can get an answer informally by doing the polynomial division like in high school, but I don't know if this is the right answer and in case it is I cannot prove it. Any help would be largely appreciated.
 
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Recall that if a function is analytic on a domain, then its Laurent series and Taylor series are identical. Do you know how to do the Taylor series expansion?
 

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