TITLE: Books about harmonic numbers
QUESTION [12 upvotes]: I'm looking for books about harmonic numbers, where I could find proofs of results about them. For example a proof for the fact, that the generating function of the generalized harmonic numbers is
$$
\sum_{n=1}^\infty  H_{n}^{(m)} z^n = \frac {\mathrm{Li}_m(z)}{1-z}.
$$
I'm also interested in particular evaluations of sums involving harmonic numbers, like this:
$$
\sum_{n=1}^{\infty}\frac{H_n}{n^2 2^n}=\zeta(3)-\frac{1}{2}\ln(2)\zeta(2).
$$
I'm also interested in sums of generalized harmonic numbers and also alternating harmonic numbers.

REPLY [3 votes]: For a multitude of problems on infinite sums involving the harmonic and generalised harmonic numbers, so-called Euler sums, you cannot go pass Cornel Ioan Valean's latest book: (Almost) Impossible Integrals, Sums, and Series.
Solutions to all problems are given and some of the sums are very challenging indeed. It is an absolute must have book if you are seriously interested in such things.
Update
You may also consider having a look at Ali Shadhar Olaikhan's book An Introduction To The Harmonic Series And Logarithmic Integrals: For High School Students Up To Researchers.