Prelude
Be $U \subset X$, where $U$ is open and $X$ is a complex manifold.
A meromorphic function $f$ over $U$ is a holomorphic function over $U \backslash S$ (Where $\bar{S}$ has no interior) such that $\exists$ an open cover of $U$ ($U = \bigcup_i U_i$) and $$f\Big|_{U_i} = \dfrac{g_i}{h_i}$$ where $g_i$ and $h_i$ are holomorphic functions over $U_i$.
Question
How can I apply this definition to the meromorphic Gamma Function? That is, what are two functions $g_i$ and $h_i$ such that $$\Gamma(z) = \dfrac{g}{h}$$
Any reference will be appreciated!
