# 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

1 year, 10 months ago

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