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