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New posts in Harmonic Numbers
Prove $\sum_{n=0}^\infty(-1)^n(\overline{H}_n-\ln2)^3=-\frac5{16}\zeta(3)$
May 08, 2021
Prove $\sum_{n=0}^\infty(-1)^n(\overline{H}_n-\ln2)^2=\frac{\pi^2}{24}$
May 08, 2021
What do you get when you sum over the smaller half of the harmonic series?
May 08, 2021
How to evaluate: $\int_0^1 \frac{\frac{\pi^2}{6}-\operatorname{Li}_2(1-x)}{1-x}\cdot \ln^2(x) \, \mathrm dx$
May 08, 2021
Find Harmonic Numbers for Imaginary and Complex Values
May 07, 2021
Calculating $\int_0^1\frac{1}{1+x}\operatorname{Li}_2\left(\frac{2x}{1+x^2}\right)dx$
May 07, 2021
How to prove that $ -n \int _0 ^1 x^{n-1} \log(1-x)dx$ equals the $n$-th harmonic number?
May 07, 2021
Challenging Sum: compute $\sum_{n=1}^\infty\frac{H_n}{2n+1}\left(\zeta(3)-H_n^{(3)}\right)$
May 07, 2021
Sum of Scaled Harmonic Numbers
May 07, 2021
How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$
May 07, 2021
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