Jensen's Formula

Theorem
Let $S$ be an open subset of the complex plane containing the closed disk:
 * $D_r = \left\{ {z \in \C : \left\vert{z}\right\vert \le r}\right\}$

of radius $r$ about $0$.

Let $f: S \to \C$ be holomorphic on $S$.

Let $f$ have no zeroes on the circle $\left\vert{z}\right\vert = r$.

Let $f \left({0}\right) \ne 0$.

Let $\rho_1, \ldots, \rho_n$ be the zeroes of $f$ in $D_r$, counted with multiplicity.

Then:
 * $(1): \quad \displaystyle \frac 1 {2 \pi} \int_0^{2 \pi} \ln \left\vert{f \left({r e^{i \theta} }\right)}\right\vert \, \mathrm d \theta = \ln \left\vert{f \left({0}\right)}\right\vert + \sum_{k \mathop = 1}^n \left({\ln r - \ln \left\vert{\rho_k}\right\vert}\right)$