Cauchy's integral theorem
Formulation on simply connected regions

Let U ⊆ C {\displaystyle U\subseteq \mathbb {C} } be a simply connected open set, and let f: U → C {\displaystyle f:U\to \mathbb {C} } be a holomorphic function. Let γ: → U {\displaystyle \gamma :\to U} be a smooth closed curve. Then:

(The condition that U {\displaystyle U} be simply connected means that U {\displaystyle U} has no "holes", or in other words, that the fundamental group of U {\displaystyle U} is trivial.)
punctuation:no_comma, detectable_content:number_placeholders[5], length_constraints:number_words[130]