In this post Another way of expressing $\sum_{k=0}^{n} \frac{H_{k+1}}{n-k+1}$ I asked for a solution of the non-alternating series. How about the alternating series? Can we find a nice way of expressing this sum? $$\sum_{k=0}^{n} (-1)^k\frac{H_{k+1}}{n-k+1}$$
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Didn't you try to mimic my previous answer ?. – Felix Marin Sep 09 '14 at 19:27
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@FelixMarin I think it's a bit more complicated since it appears $\log(1-x) \log(1+x)$ in the numerator of the generating function. – user 1591719 Sep 09 '14 at 20:00
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I know because I was trying to imitate my previous answer. We got some sum with Digamma's, etc... – Felix Marin Sep 10 '14 at 02:04