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Q32Section II (Mathematics)32 of 180

Residue at a third-order pole

The value of the integral ∮γz3(z−3)3 dz\displaystyle\oint_\gamma \frac{z^3}{(z-3)^3}\,dz, where γ(t)=2eit\gamma(t)=2e^{it}, t∈[0,2π]t\in[0,2\pi] is:

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