\begin{definition}[Definition:Exponent of Convergence]
Let $\sequence {a_n}$ be a sequence of nonzero complex numbers.
The '''exponent of convergence''' of $\sequence {a_n}$ is the infimum of $\tau \ge 0$ for which the series $\ds \sum_{n \mathop = 1}^\infty \size {a_n}^{-\tau}$ converges.
The '''exponent of convergence''' of a finite sequence is $0$.
\end{definition}