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edited body

edited May 11 at 3:04

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How to prove that $ \sum_{k=1}^\infty \frac{\sin kx}{k^z} = \frac{1}{\Gamma(z)} \int_0^\infty \frac{t^{z-1}e^t\sin x}{1–2e^t\cos x+e^{2t}}dt? $

I need it to show that $\displaystyle\sum_{k=1}^\infty \frac{\sin k}{k^3} = \frac{2\pi^2-3\pi+1}{12}$

sequences-and-series integration

asked May 11 at 2:56

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