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A peculiar Euler sum
I would like a hand in the computation of the following Euler sum
$$ S=\sum_{m,n\geq 0}\frac{(-1)^{m+n}}{(2m+1)(2n+1)^2(2m+2n+1)} \tag{1}$$
which arises from the computation of $\int_{0}^{1}\frac{\...
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3
votes
1
answer
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Generating function of forth powers of harmonic numbers.
Let $x\in (-1,1)$ and let $n\ge 1$ be an integer. Now, let us define a following family of harmonic sums:
\begin{eqnarray}
S^{(n)}(x):= \sum\limits_{m=1}^\infty [H_m]^n \cdot x^m
\end{eqnarray}
It is ...
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