Proposition 2

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

For every complex number $z$ not an integer $\leqslant 0$ and for every integer $p > 0$ one has

\Gamma \left( \frac{z}{p} \right) \Gamma \left( \frac{z+1}{p} \right) \ldots \Gamma \left( \frac{z+p-1}{p} \right) = (2\pi)^{(p-1)/2}\ p^{\frac{1}{2}-z}\ \Gamma(z)

(Legendre-Gauss multiplication formula).

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

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