Here is a theorem from Conway's Complex Analysis Book:
5.4 Cauchy’s Integral Formula (First Version) Let $G$ be an open subset of the plane and $f \colon G \to \mathbb{C}$ an analytic function. If $\gamma$ is a closed rectifiable curve in $G$ such that $n(\gamma;w) = 0$ for all $w \in \mathbb{C} - G$, then for $a \in G - \{\gamma\}$ $$ n(\gamma;a) f(a) = \frac{1}{2 \pi i} \int_\gamma \frac{f(g)}{z-a} \,\mathrm{d}z. $$ (Original scanned picture here.)
What is the $g$ and to what set does it belong? The form of this theorem I am familiar with is this:
$$ f(z) \operatorname{Ind}_\gamma(z) = \frac{1}{2 \pi i} \int_\gamma \frac{f(\zeta)}{\zeta - z} \,\mathrm{d}\zeta $$