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I am wondering about the following:

Let C be the circle |z| = 3. the contour integral

g(w) = integral on C of (2*z^2-z-2/z-w)dz can be evaluated by cauchy's integral formula. I am wondering what happens if w is greater than 3.

Would you get this: f = 2*z^2-z-2. This is an entire function.

because the contour integral of an analytic function f around 2 simply connected contours is equal, so for a contour C2 that is greater than |z| = 3, the integral of f over that contour would be equal to the integral of f over contour C. So, this means that g(w) would still give you the value of the contour integral even though your contour covered a greater area than |z| = 3. So, this would mean that for w > 3, you can still use the Cauchy formula and get 2*pi*i*2*w^2-w-2? Thanks very much.