Difference between revisions of "Barnes G at positive integer"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$G(n) = \left\{ \begin{array}{ll}...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$G(n) = \left\{ \begin{array}{ll} | $$G(n) = \left\{ \begin{array}{ll} | ||
0&\quad n=-1,-2,\ldots \\ | 0&\quad n=-1,-2,\ldots \\ | ||
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\end{array} \right.$$ | \end{array} \right.$$ | ||
where $G$ denotes the [[Barnes G]] function and $i!$ denotes the [[factorial]]. | where $G$ denotes the [[Barnes G]] function and $i!$ denotes the [[factorial]]. | ||
| − | + | ||
| − | + | ==Proof== | |
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| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
Revision as of 05:48, 6 June 2016
Theorem
The following formula holds: $$G(n) = \left\{ \begin{array}{ll} 0&\quad n=-1,-2,\ldots \\ \displaystyle\prod_{i=0}^{n-2} i!&\quad n=0,1,2,\ldots, \end{array} \right.$$ where $G$ denotes the Barnes G function and $i!$ denotes the factorial.
