\begin{definition}[Definition:Rank of Entire Function]
Let $f: \C \to \C$ be an entire function.
Let $\sequence {a_n}$ be the sequence of non-zero zeroes of $f$, repeated according to multiplicity.
The '''rank''' of $f$ is:
:the smallest positive integer $p \ge 0$ for which the series $\ds \sum_{n \mathop = 1}^\infty \size {a_n}^{-p - 1}$ converges
or:
:$\infty$ if there is no such integer.
If $f$ has finitely many zeroes, its '''rank''' is $0$.
\end{definition}