query: Formula for the general case of $\sum_{n=1}^\infty \frac{H_n}{n^2} = 2\zeta(3)$
positive_passages.docid: 20550
positive_passages.text: Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$
negative_passages.docid: 118456
negative_passages.text: Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$
negative_passages.docid: 54432
negative_passages.text: What can be said about $\prod_{s=2}^{\infty} \zeta(s) $?
negative_passages.docid: 24373
negative_passages.text: Hint on computing the series $\sum_{n=2}^\infty \frac{1}{n^2-1}$.
negative_passages.docid: 35036
negative_passages.text: Series $\sum_{n=1}^{\infty}\frac{\cos(nx)}{n^2}$
negative_passages.docid: 44970
negative_passages.text: Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
negative_passages.docid: 64223
negative_passages.text: Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$
negative_passages.docid: 32866
negative_passages.text: How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
negative_passages.docid: 121617
negative_passages.text: Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$
negative_passages.docid: 111705
negative_passages.text: Why does $\frac{1+t}{(1-t)^3}=\sum_{n=0}^{\infty}(1+n)^2t^n$
negative_passages.docid: 148940
negative_passages.text: $\sum_{n=1}^\infty\frac1{n^6}=\frac{\pi^6}{945}$ by Fourier series of $x^2$
negative_passages.docid: 22524
negative_passages.text: Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
negative_passages.docid: 145798
negative_passages.text: Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$
negative_passages.docid: 14306
negative_passages.text: What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$
negative_passages.docid: 25395
negative_passages.text: Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
negative_passages.docid: 18796
negative_passages.text: How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$?
negative_passages.docid: 67271
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$