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Mathematics
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whitexlotus
  • Member for 7 years, 2 months
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16
Rare Integral $\int_0^1 \frac{\cosh \left( \alpha \cos ^{-1}x \right)\cos \left( \alpha \sinh ^{-1}x \right)}{\sqrt{1-x^{2}}} dx$
Aug 24, 2017
11
Find the lowest value of $n$, such that the equation $p^{2}+pq+q^{2}=n$ has only five solutions
Jun 29, 2017
8
Alternative proof that $\frac{\sqrt[3]3}{\sqrt[2]2}\cdot\frac{\sqrt[5]5}{\sqrt[4]4}\cdot\frac{\sqrt[7]7}{\sqrt[6]6}\cdot ...=2^{-\gamma+\log\sqrt2}$
Aug 20, 2017
4
Rare sum with Trigamma function $\left( -1 \right)^{n-1}\left( \psi _{1}\left( n \right) \right)^{2}$
Aug 31, 2017
3
Inequality $\frac{x_1^2}{x_1^2+x_2x_3}+\frac{x_2^2}{x_2^2+x_3x_4}+\cdots+\frac{x_{n-1}^2}{x_{n-1}^2+x_nx_1}+\frac{x_n^2}{x_n^2+x_1x_2}\le n-1$
Aug 1, 2017
3
Inequality $\frac{1}{a+b}+\frac{1}{a+2b}+...+\frac{1}{a+nb}<\frac{n}{\sqrt{a\left( a+nb \right)}}$
Aug 1, 2017
3
Dilogarithm integral $\int_0^{\infty} \frac{x^{s/2-1}}{1+x^s} \text{Li}_2(-x) dx=- \frac{\pi^3}{4} \left( \frac1{3 s}+ \frac1{ s^3}\right)$
Aug 20, 2017
3
Hard Integral $\int\limits_0^1 \frac{\ln y\operatorname{Li}_2 (-y)}{1-y^2} \, dy$
Aug 31, 2017
2
Hard inequality with cos() and sin()
Aug 1, 2017
2
Calculate the closed form of $\frac{\sqrt[5]{5}}{\sqrt[3]{3}}\cdot \frac{\sqrt[9]{9}}{\sqrt[7]{7}}\cdot \frac{\sqrt[13]{13}}{\sqrt[11]{11}}\cdot ...$
Aug 7, 2017