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Kirill

Apparently, this user prefers to keep an air of mystery about them.

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  • ikirill
  • Member for 8 years
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28 Closed form for $\int_0^\infty\left(\int_0^1\frac1{\sqrt{1-y^2}\sqrt{1+x^2\,y^2}}\mathrm dy\right)^3\mathrm dx.$ May 29 '13
28 How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$? May 29 '13
27 Approximate value of a slowly-converging sum of $\sum|\sin n|^n/n$ Jun 22 '14
26 Closed form for $\sum_{n=1}^\infty\frac{\psi(n+\frac{5}{4})}{(1+2n)(1+4n)^2}$ Jun 4 '13
25 Is there a simpler closed form for $\sum_{n=1}^\infty\frac{(2n-1)!!\ (2n+1)!!}{4^n\ (n+2)\ (n+2)!^2}$ May 27 '13
24 How to prove $\int_0^\infty J_\nu(x)^3dx\stackrel?=\frac{\Gamma(1/6)\ \Gamma(1/6+\nu/2)}{2^{5/3}\ 3^{1/2}\ \pi^{3/2}\ \Gamma(5/6+\nu/2)}$? May 28 '13
22 Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$ Oct 25 '13
21 Computing $\lim\limits_{n\to\infty} \Big(\sum\limits_{i = 1}^n \sum\limits_{j = 1}^n \frac1{i^2+j^2}-\frac{\pi}{2} \log(n)\Big)$. Sep 25 '14
21 How to prove $4\times{_2F_1}(-1/4,3/4;7/4;(2-\sqrt3)/4)-{_2F_1}(3/4,3/4;7/4;(2-\sqrt3)/4)\stackrel?=\frac{3\sqrt[4]{2+\sqrt3}}{\sqrt2}$ May 24 '13
20 How can I prove this closed form for $\sum_{n=1}^\infty\frac{(4n)!}{\Gamma\left(\frac23+n\right)\,\Gamma\left(\frac43+n\right)\,n!^2\,(-256)^n}$ May 26 '13
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