Large powers of sine appear Gaussian -- why? – math.stackexchange.com

Large powers of sine appear Gaussian -- why? – math.stackexchange.com

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As part of approximating an integral, I have noticed that $\sin^k(x), x\in[0, \pi]$ look almost identical to $\exp\left(-\frac{k}{2}(x-\frac{\pi}{2})^2\right)$ once $k$ is large enough (in practice, ...

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