Bourbaki

Proposition 1

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

Functions of a Real Variable, chapter VII, § 2. THE GAMMA FUNCTION IN THE COMPLEX DOMAIN

For every complex zz one has

1Γ(z)Γ(1−z)=1πsin⁡πz \frac{1}{\Gamma(z)\Gamma(1-z)} = \frac{1}{\pi} \sin \pi z

(the complements' relation).

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

Cited by

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Cites

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Transcribed from the printed volume. Not translated.