Mathematics Tripos Papers

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4.I.8B

Complex Methods | Part IB, 2003

Find the Laurent series centred on 0 for the function

f(z)=1(z−1)(z−2)f(z)=\frac{1}{(z-1)(z-2)}f(z)=(z−1)(z−2)1​

in each of the domains (a) ∣z∣<1|z|<1∣z∣<1, (b) 1<∣z∣<21<|z|<21<∣z∣<2, (c) ∣z∣>2|z|>2∣z∣>2.

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