7. Remark 2.12.2 - products are delicate

\prod_{n = 1}^{\infty} (1 - \frac{z^{2}}{n^{2}})

converges absolutely for any $z \in C$ , since the series $- z^{2} \sum_{n = 1}^{\infty} \frac{1}{n^{2}}$ converges absolutely.

HOWEVER:
2. The infinite product

\prod_{n = 1}^{\infty} (1 - \frac{z}{n}) (1 + \frac{z}{n})

is 1;;not absolutely convergent! It behaves like a sum of harmonic series'.