Complex antiderivative
= Complex antiderivative
{title2=$F'=f$}
A <holomorphic function> $F$ on a domain with complex derivative $F'=f$. Its <contour integral> satisfies $\int_\gamma f(z)\,dz=F(\gamma(b))-F(\gamma(a))$ by the <chain rule> along each smooth contour segment. In particular every closed contour has integral zero. Having local complex antiderivatives need not provide a single one on a domain with holes.