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Infiniticism
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  • Militaireetmari
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要扫除一切害人虫，全无敌！

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50
Evaluate $\int_{-\infty}^\infty\frac{x}{\sin^2(\sqrt{x})\sinh^2\left(2\sqrt{2x}\right)+\pi^2\cos^2(\sqrt{x})\cosh^2\left(2\sqrt{2x}\right)}\mathrm dx$
Oct 2, 2020
34
Prove $\int_0^{\infty }\frac1{\sqrt{x}}\left(\frac{\cos(\pi x^2)}{\sinh (\pi x)}-\frac1{\pi x}\right)dx=\frac{1}{\sqrt{2}}\zeta(\frac{1}{2})$
Sep 9, 2020
22
What is $\, _4F_3\left(1,1,1,\frac{3}{2};\frac{5}{2},\frac{5}{2},\frac{5}{2};1\right)$?
Sep 6, 2020
21
Proving $\int_{\sqrt{\frac{3}{5}}}^1 \frac{\arctan (x)}{\sqrt{2 x^2-1} \left(3 x^2-1\right)} \, dx=\frac{3 \pi ^2}{160}$
Aug 22, 2019
19
Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$
Jun 3, 2020
19
Evaluate hypergeometric $_6F_5\left(\{\frac12\}_3,\{1\}_3;\{\frac32\}_5;1\right)$
Jun 30, 2020
17
Evaluate $\int_{(-\infty,\infty)^n}\frac{\prod_{k=1}^n \sin(a_k x_k)}{\prod_{k=1}^n x_k}\frac{\sin(\sum_{k=1}^n a_k x_k)}{\sum_{k=1}^n a_k x_k}$
Feb 25, 2020
16
A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations
Mar 31, 2020
15
Evaluate hypergeometric $_6F_5\left(\{\frac12\}_3,\{1\}_3;\{\frac32\}_5;1\right)$
Jun 27, 2020
15
Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$
Aug 17, 2020
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