I've seen a few posts already discussed about this problem but i want to know is there another way to solve without using residue theorem ,because it may be a challenge for me if it's possible to solve $$\sum_{n=1}^{\infty} \frac{1}{n^3\sin(\sqrt2n\pi)}.$$
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1Maybe link to the posts you've seen on this problem? – NoName Mar 30 '21 at 12:18
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2here https://math.stackexchange.com/questions/1658250/compute-the-series-sum-n-1-infty-frac1n3-sinn-pi-sqrt2 https://math.stackexchange.com/questions/3925348/prove-sum-n-1-infty-frac1n3-sinn-pi-sqrt2-frac13-pi3360-sqr?noredirect=1&lq=1 – Unik Sillavich Mar 30 '21 at 12:20
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@Riemann Seriously, do you think that’s a valuable edit? – Ted Shifrin Nov 19 '22 at 02:44
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@Ted Shifrin Yes, I think so !! – Riemann Nov 19 '22 at 03:03
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@Riemann Editing a question bumps it back to the front page. Making small, relatively inconsequential edits to old questions doesn't really do much to help improve the overall quality of the site. For something like this, which really doesn't meet the quality standards for the site, and which is a duplicate question, it is generally better to let it go. – Xander Henderson Nov 19 '22 at 13:00