# More general reflection formula for Gamma function

It is know that $\Gamma(z)\, \Gamma{(1-z)}=\pi \csc( \pi z)$. Is there any formula for $\Gamma{(a+z)}\Gamma{(a-z)}$ where $a$ is a rational number, i. e., $a=p/k$ with $p, k$ integers and $z$ is a complex number ?

-
But it does not look to me as a generalization because there is no $a$ that you can plug into $\Gamma{(a+z)}\Gamma{(a-z)}$ to get $\Gamma(z)\, \Gamma{(1-z)}$? –  user67878 Mar 27 '13 at 15:20
But try to explore what you have here : Gamma function as a starting point. –  user67878 Mar 27 '13 at 15:28
For a=0 or a=1 the expression $\Gamma{(a+z)} \Gamma{(a-z)}$ can be expressed in terms of the reflection formula above. But what about $a \neq 0$ or $a\neq 1$ ? –  ice Mar 27 '13 at 15:52