Convergence of gamma function at positive values

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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.

Proof

References