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

Definition
Let $\left\langle{a_n}\right\rangle$ be a sequence in $\C$.

Let $\log$ denote the complex logarithm.

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

Also see

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