2
$\begingroup$

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?

$\endgroup$
3
  • 1
    $\begingroup$ Are you asking for Euler's proof specifically, or just any proof? $\endgroup$ – vrugtehagel Jun 20 '19 at 9:13
  • $\begingroup$ 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. $\endgroup$ – MikeGp Jun 20 '19 at 9:31
  • $\begingroup$ The linked question explicitly asked for Euler's approach. $\endgroup$ – YuiTo Cheng Jun 20 '19 at 9:56