Difference between revisions of "Gamma function diverges at infinity"
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(Created page with "==Theorem== If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then $$\displaystyle\lim_{x \rightarrow \infty} \Gamma_{\mathbb{T}}(x;s) = \infty.$$ ==Proof== ==R...") |
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==Theorem== | ==Theorem== | ||
If $\mathbb{T}$ is a [[time scale]] and $s \in \mathbb{T}^+$, then | If $\mathbb{T}$ is a [[time scale]] and $s \in \mathbb{T}^+$, then | ||
| − | $$\displaystyle\lim_{x \rightarrow \infty} \Gamma_{\mathbb{T}}(x;s) = \infty | + | $$\displaystyle\lim_{x \rightarrow \infty} \Gamma_{\mathbb{T}}(x;s) = \infty,$$ |
| + | where $\Gamma_{\mathbb{T}}$ denotes the [[gamma function]]. | ||
==Proof== | ==Proof== | ||
Latest revision as of 17:56, 15 January 2023
Theorem
If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then $$\displaystyle\lim_{x \rightarrow \infty} \Gamma_{\mathbb{T}}(x;s) = \infty,$$ where $\Gamma_{\mathbb{T}}$ denotes the gamma function.
