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Symmetry of Euler sums

Let \zeta denote the Riemann zeta function. Prove that

    \[\sum_{n=1}^{\infty} \frac{\mathcal{H}_n^{(k)}}{n^k} = \frac{\zeta(2k)+ \zeta^2(k)}{2}\]

where \mathcal{H}_n^{(s)} is the generalized harmonic number of order s.

Solution

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