# Jensen's Formula for Arbitrary Neighborhoods

The Jensen's formula says the following: Let $$f$$ be analytic on the disc $$D$$ of radius $$R$$ centered at the origin such that $$f(0)\neq 0$$, then \begin{align} \log(|f(0)|)+ \sum_{i=1}^n \log \left(\frac{R}{a_i} \right ) = \frac{1}{2\pi}\int_0^{2\pi}\log(|f(Re^{i\theta})|)d\theta, \end{align} where $$a_i$$'s are zerof of $$f$$ in $$D$$.

Are there extensions of this theorem to regions other than discs. For example, does it hold of rectangular regions?

• I suppose a good start is with precomposing with some conformal maps of your choice to see how the formula changes. Jun 19 '19 at 0:02