From Wikipedia, the upper incomplete gamma function is defined as: $$\Gamma(s,x) = \int_x^{\infty} t^{s-1}\,e^{-t}\,{\rm d}t ,\,\!$$ whereas the lower incomplete gamma function is defined as: $$\gamma(s,x) = \int_0^x t^{s-1}\,e^{-t}\,{\rm d}t .\,\!$$ I'm trying to estimate from above $$\left|\gamma(n,z)-\gamma(n,-z)\right|$$ where $n\in\mathbb N$ and $z$ is an imaginary number but I have no idea.
Any suggestions please?