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I'm having trouble progressing through (in my experience) the tedious calculations required to obtain a Laurent Expansion of a complex function. enter image description here

The problem arises in finding the series within the annulus. Thank you in advanced for your help.

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  • $\begingroup$ After looking at other questions within the Laurent Series tag, I realise that these questions are solved using methods other than what my book has described. My book uses the fact that the series is the sum of two series where the coefficients are given by integrals. $\endgroup$ Commented Oct 7, 2013 at 5:58

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Hint for (a): where are the singularities of $f(z)$?

Hint for (b): partial fractions.

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  • $\begingroup$ Ok, I just need help with the annulus. That is 2<|z+1|<3. I've used partial fractions but I'm unsure of how to manipulate my expression to create convergence. @Robert Israel $\endgroup$ Commented Oct 7, 2013 at 10:17

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