Multi-factorials are handy. Sometimes results can be expressed compactly by introducing a double factorial or possibly higher factorial. For example
$$\int_0^{\pi/2} \sin^{2n+1} \theta \:\: d\theta = \frac{(2n)!! }{ (2n+1)!!}$$
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Multi-factorials are handy. Sometimes results can be expressed compactly by introducing a double factorial or possibly higher factorial. For example $$\int_0^{\pi/2} \sin^{2n+1} \theta \:\: d\theta = \frac{(2n)!! }{ (2n+1)!!}$$ |
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