iterated harmonic numbers vs Riemann zeta – mathoverflow.net

iterated harmonic numbers vs Riemann zeta – mathoverflow.net

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Define the $m$-th iterated harmonic sums in the manner: $\bar{H}_0(n):=1$ and for $m\geq1$ by $$\bar{H}_m(n):=\sum_{k=1}^n\frac{\bar{H}_{m-1}(k)}k.$$ For example, $\bar{H}_1(n)=\sum_{k=1}^n\frac1k$ ...

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