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 $x \in \mathbb{R}^+$.
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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==

Latest revision as of 17:53, 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.

Proof

References