Difference between revisions of "Beta in terms of sine and cosine"
From specialfunctionswiki
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$B(x,y)=2 \displaystyle\int_0^{\frac{\pi}{2}} (\sin t)^{2x-1}(\cos t)^{2y-1} | + | $$B(x,y)=2 \displaystyle\int_0^{\frac{\pi}{2}} (\sin t)^{2x-1}(\cos t)^{2y-1} \mathrm{d}t,$$ |
where $B$ denotes the [[beta function]], $\sin$ denotes the [[sine]] function, and $\cos$ denotes the [[cosine]] function. | where $B$ denotes the [[beta function]], $\sin$ denotes the [[sine]] function, and $\cos$ denotes the [[cosine]] function. | ||
Revision as of 00:34, 4 June 2016
Theorem
The following formula holds: $$B(x,y)=2 \displaystyle\int_0^{\frac{\pi}{2}} (\sin t)^{2x-1}(\cos t)^{2y-1} \mathrm{d}t,$$ where $B$ denotes the beta function, $\sin$ denotes the sine function, and $\cos$ denotes the cosine function.
