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Any method for this double harmonic sum?

\[\displaystyle \sum_{m=1}^{\infty}\sum_{n=1}^{\infty} \frac{(-1)^{m-1}{\rm H}_m{\rm H}_n}{(m+1)(n+1)(m+n-1)^3}\]

\[\] Notation: \( \rm H_n\) denotes the \(n^\text{th} \) harmonic number, \( \rm H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n\).


This is a part of the set Formidable Series and Integrals

Note by Aditya Sharma
3 months, 4 weeks ago

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