query: Evaluate the sum $\sum ^{\infty}_{n=1} \frac{1}{n^2+a^4}$
positive_passages.docid: 138313
positive_passages.text: How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
negative_passages.docid: 76387
negative_passages.text: Evaluate the series $\sum_{n=1}^{\infty} \frac{2^{[\sqrt{n}]}+2^{-[\sqrt{n}]}}{2^n}$
negative_passages.docid: 150563
negative_passages.text: Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$
negative_passages.docid: 37007
negative_passages.text: Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
negative_passages.docid: 60104
negative_passages.text: Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
negative_passages.docid: 93690
negative_passages.text: How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
negative_passages.docid: 156720
negative_passages.text: Evaluate $\sum_ {n=1}^{\infty} \cot^{-1}(2n^2)$
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 34637
negative_passages.text: Evaluating $\sum\frac{\sin(n)}{n^a}$
negative_passages.docid: 49936
negative_passages.text: Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$
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: 43509
negative_passages.text: Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$
negative_passages.docid: 127189
negative_passages.text: sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
negative_passages.docid: 48233
negative_passages.text: Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
negative_passages.docid: 52987
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
negative_passages.docid: 9610
negative_passages.text: Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
negative_passages.docid: 152698
negative_passages.text: Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$