Cauchy's formula with singularities on the curve

Question

One knows that the Cauchy's formula asserts that for a given open set $\Omega\subseteq\mathbb{C}$ and $\gamma$ is a simply connected curve contained in $\Omega$, then $$f(z)=\int_{\gamma}\frac{f(\xi)}{\xi-z}d\xi$$ for all $z$ in the interior of $\gamma$. I wonder what may happen if $z$ is chosen on the curve? Obviously, the integral above is not well defined. Is there another definition such that the right-hand side makes sense? I would appreciate any related hint.