Theorem 1

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

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

For every complex number $z$ not an integral multiple of $\pi$ one has

\cot z = \frac{1}{z} + \sum_{n=1}^{\infty} \frac{2z}{z^2 - n^2 \pi^2}

(the series on the right being normally convergent on every compact subset $K \subset \mathbf{C}$ not containing any integer multiple of $\pi$ (Eulerian expansion of $\cot z$ ).)

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

Cited by

§ 2. EULERIAN EXPANSIONS OF THE TRIGONOMETRIC FUNCTIONS AND BERNOULLI NUMBERS

Cites

Nothing.