= Blaschke factor
{c}
{title2=$\psi_{w,R}(z)=R(z-w)/(R^2-\overline wz)$}
For $|w|<R$, this <Möbius transformation> maps the radius-$R$ disc to the unit disc, vanishes at $w$ and has modulus one on the boundary. Expanding gives $|R^2-\overline wz|^2=R^2|z-w|^2$ when $|z|=R$; its <pole> lies outside the disc. Dividing a <holomorphic function> by factors corresponding to its interior zeros removes those zeros without changing its boundary modulus. This gives a direct factorization proof of <Jensen's formula>.
Back to article page
