Difference between revisions of "Barnes G at positive integer"
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$$G(n) = \left\{ \begin{array}{ll} | $$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]]. | ||
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.
