Theorem 2

Tag 08IG, permanent. Cite it as [Bourbaki, Tag 08IG].

Functions of a Real Variable, chapter VI, § 2. EULERIAN EXPANSIONS OF THE TRIGONOMETRIC FUNCTIONS AND BERNOULLI NUMBERS

For every complex number $z$ one has

\sin z = z \prod_{n=1}^{\infty} \left( 1 - \frac{z^2}{n^2 \pi^2} \right)

the infinite product on the right being absolutely and uniformly convergent on every compact subset of $\mathbf{C}$ (Eulerian expansion of $\sin z$ ).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.