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.
2026-03-29 10:59:58.1774781998
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Books about harmonic numbers
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You might be interested in Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values, by Jianqiang Zhao.
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Zeta and q-Zeta Functions and Associated Series and Integrals (Elsevier Insights) and the papers referenced therein regarding harmonic numbers and generalised harmonic numbers has a fair bit of info.