Question
Evaluate the integral
where C is any simple closed curve enclosing .
Answer :
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The integral is [ \oint_C \frac{5z^2 - 3z + 2}{(z-1)^3} , dz ] Here, the integrand has a pole of order 3 at (z = 1). For a pole of order (n), the residue formula is [ \text{Res}\left(f, z_0\right) = \frac{1}{(n-1)!} \lim_{z \to z_0} \frac{d^{,n-1}}{dz^{,n-1}} \big[ (z-z_0)^n f(z) \big]. ]
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