Books about harmonic numbers

sequences-and-series calculus reference-request book-recommendation harmonic-numbers

You might be interested in Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values, by Jianqiang Zhao.


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.


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.

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