Convergence of gamma function at positive values
From timescalewiki
Theorem
If $\mathbb{T}$ be a time scale and $s \in \mathbb{T}^+$, then $\Gamma_{\mathbb{T}}(x;s)$ converges for any $x \in \mathbb{R}^+$, where $\Gamma_{\mathbb{T}}$ denotes the gamma function.
