ThmDex – An index of mathematical definitions, results, and conjectures.
Goursat's theorem
Formulation 0
Let $U \subseteq \mathbb{C}$ be a D5008: Standard open complex set such that
(i) $f : U \to \mathbb{C}$ is a D1392: Holomorphic function on $U$
(ii) $T \subseteq \mathbb{C}$ is a D4996: Complex triangle
(iii) \begin{equation} \text{int}(T) \subseteq U \end{equation}
Then \begin{equation} \int_T f(z) \, d z = 0 \end{equation}