Complex Conjugate of Gamma Function
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Theorem
Let $\Gamma$ denote the gamma function.
Then:
- $\forall z \in \C \setminus \set {0, -1, -2, \ldots}: \map \Gamma {\overline z} = \overline {\map \Gamma z}$
Proof
This is immediate from, say, the Euler form of $\Gamma$ and the fact that complex conjugation preserves products and sums.