The integral comes from the physics $$ I=\int^{+i\infty}_{-i\infty} dz_1 \int^{+i\infty}_{-i\infty} dz_2 \Gamma(-z_1)\Gamma(-z_2)\Gamma(-z_1-z_2)$$
I want to use residue theorem, since the Euler gamma function $\Gamma(-n)$ has simple pole at positive integre $n$. Here the trouble is that when I try to do the integral one by one, for example, when I integrate $z_1$ first, the $z_2$ is not a nonzero parameter always.