Definition:Absolute Convergence of Product/Complex Numbers/Definition 3

Definition
Let $\sequence {a_n}$ be a sequence in $\C$.

The infinite product $\ds \prod_{n \mathop = 1}^\infty \paren {1 + a_n}$ is absolutely convergent there exists $n_0 \in \N$ such that:
 * $a_n \ne -1$ for $n > n_0$
 * The series $\ds \sum_{n \mathop = n_0 + 1}^\infty \log \paren {1 + a_n}$ is absolutely convergent

where $\log$ denotes the complex logarithm.

Also see

 * Equivalence of Definitions of Absolute Convergence of Product of Complex Numbers