Thread: Does this function even exist?

Find a function f and a simple closed contour C so that f is analytic in a neighborhood of C, but $\displaystyle \oint_Cf$is not 0.

Any help on this?

Originally Posted by paupsers

Find a function f and a simple closed contour C so that f is analytic in a neighborhood of C, but $\displaystyle \oint_Cf$is not 0.

Any help on this?

Take the unit circle as $\displaystyle C$, $\displaystyle f(z)=\frac{1}{z}$.