Gamma function diverges at infinity

Theorem

If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then $$\displaystyle\lim_{x \rightarrow \infty} \Gamma_{\mathbb{T}}(x;s) = \infty,$$ where $\Gamma_{\mathbb{T}}$ denotes the gamma function.