A harmonic function equals both its circular average and its disc average at the center.Suggest a slogan
Let \(\Omega\subseteq\CC\) be open, let \(u\) be harmonic on \(\Omega\), and let \(z_0=x_0+iy_0\in\Omega\) and \(r>0\) satisfy \(\overline{D_r(z_0)}\subseteq\Omega\). Then \[ u(z_0)=\frac{1}{2\pi r}\oint_{\bd D_r(z_0)}u\,ds=\frac{1}{\pi r^2}\iint_{D_r(z_0)}u(x,y)\dx\dy, \] where \(ds\) is arc length on the circle \(\bd D_r(z_0)\).