Is there an identity for $\Gamma(z) \Gamma(\bar {z})$?

Post-question edits:

Have you come across any, in addition to [the ones listed here](https://en.wikipedia.org/wiki/Gamma_function)? (there, special cases, where the real part of $z$ is integer or half integer, are also listed.)

[Abramowitz-Stegun](http://people.math.sfu.ca/~cbm/aands/page_257.htm) lists the following under 6.1.45 $$\lim\_{|y|\to \infty} (2\pi)^{-1/2} |\Gamma (z)| e^{\pi|y|/2} |y|^{1/2-x} =1$$