Definition 1

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

We denote by $\Gamma(x)$ the function $> 0$ which is defined on the interval $]0, +\infty[$ , that satisfies the equation

\Gamma(x+1) = x \Gamma(x),

(7) and is such that

\Gamma(1) = 1

and that

\log \Gamma(x)

is convex on

]0, +\infty[

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

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