# Questions tagged [harmonic-numbers]

For questions regarding harmonic numbers, which are partial sums of the harmonic series. The $N$-th harmonic number is the sum of reciprocals of the first $N$ natural numbers.

91 questions
186 views

128 views

### On binomial sums $\sum_{n=1}^\infty \frac{1}{n^k\,\binom {2n}n}$ and log sine integrals

Seven years ago, I asked about closed-forms for the binomial sum $$\sum_{n=1}^\infty \frac{1}{n^k\,\binom {2n}n}$$ Some alternative results have been made. Up to a certain $k$, it seems it can be ...
177 views

### A cubic nonlinear Euler sum

Any idea how to solve the following Euler sum $$\sum_{n=1}^\infty \left( \frac{H_n}{n+1}\right)^3 = -\frac{33}{16}\zeta(6)+2\zeta(3)^2$$ I think It can be solved it using contour integration but ...
174 views

117 views

### Infinite sum of harmonic number over general polynomial

As an extension to my question Infinite sum of harmonic number over polynomial of 2nd degreee I found a general formula for a polynomial of arbitrary degree which I had presented as a self answer but ...
For the purposes of this question, the Harmonic Number, $H_n$ is defined by the finite series sum $H_n=\sum_{k=1}^n\frac{1}{k}$ (n and k being positive integers) and the Harmonic Logarithm, $hlog(n)$ ...