Primitive of a holomorphic function on a simply connected domain
= Primitive of a holomorphic function on a simply connected domain
Every <holomorphic function> $f$ on a <simply connected domain> has a single-valued <antiderivative>. Fixing $z_0$ and setting
$$
F(z)=\int_{z_0}^z f(t)\,dt
$$
gives a path-independent function with $F'=f$, because the <Cauchy integral theorem> makes the integral around every closed path zero.