Difference between revisions of "Beta in terms of sine and cosine"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$B(x,y)=...") |
|||
| Line 1: | Line 1: | ||
| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$B(x,y)=2 \displaystyle\int_0^{\frac{\pi}{2}} (\sin t)^{2x-1}(\cos t)^{2y-1}dt,$$ | $$B(x,y)=2 \displaystyle\int_0^{\frac{\pi}{2}} (\sin t)^{2x-1}(\cos t)^{2y-1}dt,$$ | ||
where $B$ denotes the [[beta function]], $\sin$ denotes the [[sine]] function, and $\cos$ denotes the [[cosine]] function. | where $B$ denotes the [[beta function]], $\sin$ denotes the [[sine]] function, and $\cos$ denotes the [[cosine]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 00:34, 4 June 2016
Theorem
The following formula holds: $$B(x,y)=2 \displaystyle\int_0^{\frac{\pi}{2}} (\sin t)^{2x-1}(\cos t)^{2y-1}dt,$$ where $B$ denotes the beta function, $\sin$ denotes the sine function, and $\cos$ denotes the cosine function.
