Problem 1601 (difficulty: 6/10)

Let \(\displaystyle f\) be continuous on the closed unit disc and holomorphic in its interior. Prove that for \(\displaystyle |z|<1\)

\(\displaystyle f(z)=\frac1{2\pi i}\int_{|z|=1}\frac{f(\xi)}{z-\xi}\dxi. \)

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