If f(z) has a pole of order k at z=z0 then
rez(f,z0)=z→z0lim((k−1)!1dzk−1dk−1((z−z0)kf(z))) z=−2, simple pole
rez(f,−2)=z→−2lim((z+2)f(z))
=z→−2lim((z+2)((z+2)(z−1)21))
=z→−2lim((z−1)21)=(−2−1)21=91
z=1, order 2 pole
rez(f,1)=z→1lim((2−1)!1dz2−1d2−1((z−1)2f(z)))
=z→1lim(dzd((z−1)2((z+2)(z−1)21)))
=z→1lim(dzd(z+21))
=z→1lim(−(z+2)21)
=−(1+2)21=−91
z=−2, simple pole
rez(f,−2)=91
z=1, order 2 pole
rez(f,1)=−91
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