Difference between revisions of "Convergence of gamma function at positive values"
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==Theorem== | ==Theorem== | ||
| − | If $s \in \mathbb{T}^+$, then $\Gamma_{\mathbb{T}}(x;s)$ converges for any $x \in \mathbb{R}^+$. | + | 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== | ==Proof== | ||
Revision as of 17:52, 15 January 2023
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.
