Harmonic function as the real part of a holomorphic function
= Harmonic function as the real part of a holomorphic function
A real-valued function $u$ on a <simply connected domain> is <harmonic function>[harmonic] exactly when
$$
u=\operatorname{Re}f
$$
for some <holomorphic function> $f$. One construction observes that $u_x-iu_y$ is holomorphic and takes its <primitive of a holomorphic function on a simply connected domain>[holomorphic primitive].