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[tex]\frac{1}{2\pi i}\int_C \frac{f(\zeta)}{w(\zeta)}\frac{w(\zeta)-w(z)}{\zeta -z}d\zeta[/tex]

where f is holomorphic on the hole complex plane, where w(z) is a polynomial of degree n with all of its zeroes distinct (i.e. all n have multiplicity 1), and where C is a closed curve containing all the zeroes of w in its interior.

The solution manual says that the integral equals

[tex]\sum_{j=1}^n Res(\frac{f(\zeta)}{w(\zeta)}\frac{w(\zeta)-w(z)}{\zeta -z}, \zeta_j)[/tex]

where [itex]\zeta_j[/itex] are the n zeroes of w. But isn't [itex]\zeta = z[/itex] also a pole for the integrand?

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# Residue & pole of a function

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