Difference between revisions of "Barnes G at positive integer"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$G(n) = \left\{ \begin{array}{ll}...") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$G(n) = \left\{ \begin{array}{ll} | $$G(n) = \left\{ \begin{array}{ll} | ||
0&\quad n=-1,-2,\ldots \\ | 0&\quad n=-1,-2,\ldots \\ | ||
| − | \displaystyle\prod_{ | + | \displaystyle\prod_{k=0}^{n-2} k!&\quad n=0,1,2,\ldots, |
\end{array} \right.$$ | \end{array} \right.$$ | ||
where $G$ denotes the [[Barnes G]] function and $i!$ denotes the [[factorial]]. | where $G$ denotes the [[Barnes G]] function and $i!$ denotes the [[factorial]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 12:52, 17 September 2016
Theorem
The following formula holds: $$G(n) = \left\{ \begin{array}{ll} 0&\quad n=-1,-2,\ldots \\ \displaystyle\prod_{k=0}^{n-2} k!&\quad n=0,1,2,\ldots, \end{array} \right.$$ where $G$ denotes the Barnes G function and $i!$ denotes the factorial.
