Question Number 134750 by mnjuly1970 last updated on 06/Mar/21
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{advanced}\:\:\:{calculus}.... \\ $$$$\:\:\:{prove}\:\:\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\Sigma\frac{\mathrm{1}}{{n}^{\mathrm{3}} {sin}\left(\sqrt{\mathrm{2}}\:\pi{n}\right)}\:=\frac{−\mathrm{13}\sqrt{\mathrm{2}}\:\pi^{\mathrm{3}} \:}{\mathrm{720}} \\ $$$$\:\:\:\:\:...{m}.{n}... \\ $$