Complex Conjugate of Gamma Function
In particular: results about complex conjugation preserving products and sums.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links.
To discuss this in more detail, feel free to use the talk page.
Once you have done so, you can remove this instance of {{MissingLinks}} from the code.
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.
