Blaschke sequence
= Blaschke sequence
{c}
{title2=$\sum_n(1-|a_n|)<\infty$}
A sequence in the <unit disc>, counted with <multiplicity>, is a Blaschke sequence when it satisfies the <Blaschke condition>. The zeros of every nonzero bounded <holomorphic function> form such a sequence: <Jensen's formula> bounds $\sum_{|a_n|<r}\log(r/|a_n|)$ uniformly as $r\uparrow1$, and $1-|a|\le-\log|a|$ gives the assertion. There are only finitely many zeros at the origin, which can be factored out first.