Identities For Generalized Harmonic Number

Question

I have been searching for identities involving generalized harmonic numbers \begin{equation*}H_n^{(p)}=\sum_{k=1}^{n}\frac{1}{k^p}\end{equation*} I found several identities in terms of $H_n^{(1)}$, but I am looking for some interesting identities for $H_n^{(2)}$. Does anyone know of any identities know of any nontrivial identities for $H_n^{(2)}$? I found some listed on Wikipedia, but this list is not comprehensive. Thanks for your help.

1. integral identities
2. summation identities
3. recursive identities
4. in terms of another function

Answer 1

There is a nice list and a set of references at mathworld. Additionally, I discovered this one while writing a thesis on the Riemann Zeta function.

$$\sum_{n=1}^\infty \frac{H_n^{(s)}} {n^s}=\frac{\zeta(s)^2+\zeta(2s)}{2}.$$