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Closed form of \(\displaystyle \sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{H_n}{kn (k+n)^3}\)

Prove that: \[\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{H_n}{kn (k+n)^3}=\frac{215}{48}\zeta(6) - 3\zeta^2(3)\]

Notations:


This is a part of the set Formidable Series and Integrals.

Note by Aditya Kumar
6 months, 2 weeks ago

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