In equation $6.6$ pg. $20$ of https://www.researchgate.net/publication/318529311_Some_infinite_series_involving_hyperbolic_functions we have a nice expression $$\sum_{n=1}^{\infty}\frac{1}{n(e^{2\pi n}-1)}=\frac{1}{4}\log\left(\frac{4}{\pi}\right)-\frac{\pi}{12}+\log \Gamma \left(\frac{3}{4}\right) $$ Question: I have searched the above referenced book but could not find a proof of the above formula. Can someone please prove it or give a reference (with page number) of it?
2026-03-25 01:13:20.1774401200
Reference request for a formula
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