Does anyone know how Euler in the 18th century proved that $$ \sum_{n=1}^{\infty} \frac{H_n}{n^2}=2 \zeta(3) $$ with $H_n$ being the $n$'th harmonic number?
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1Are you asking for Euler's proof specifically, or just any proof? – Jun 20 '19 at 09:13
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I was actually asking for the classic approach. From the answers I reckon he did the more general formula with q instead of the square. – MikeGp Jun 20 '19 at 09:31
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The linked question explicitly asked for Euler's approach. – YuiTo Cheng Jun 20 '19 at 09:56