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Mathematics
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user90369
  • Member for 8 years, 3 months
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24
Evaluating integral $\int_0^1 \frac{x-x^2}{\sin \pi x} dx = \frac{7 \zeta(3)}{\pi^3}$
May 24, 2018
22
Product $\left(\frac31\right)^{1/2}\cdot\left(\frac75\right)^{1/6}\cdot \left(\frac{11}9\right)^{1/10}\cdot \left(\frac{15}{13}\right)^{1/14}\cdots$
Sep 26, 2017
18
Generalised Integral $I_n=\int_0^{\pi/2} \frac{x^n}{\sin ^n x} \ \mathrm{d}x, \quad n\in \mathbb{Z}^+.$
Jul 14, 2016
15
Prove $\int_0^1 \frac{4\cos^{-1}x}{\sqrt{2x-x^2}}\,dx=\frac{8}{9\sqrt{\pi}}\left(9\Gamma(3/4)^2{}_4F_3(\cdots)+\Gamma(5/4)^2{}_4F_3(\cdots)\right)$
Aug 23, 2017
13
Closed form of $\int_0^\infty \left(\frac{\arctan x}{x}\right)^ndx$
Oct 2, 2018
11
Prove inequality $\arccos \left( \frac{\sin 1-\sin x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$
Aug 26, 2016
9
Prove the following series $\sum\limits_{s=0}^\infty \frac{1}{(sn)!}$
Sep 27, 2016
9
List of integrals or series for Gieseking's constant $\rm{Cl}_2\big(\tfrac{\pi}3\big)$?
Jun 12, 2019
9
Evaluate $\int_{0}^{\pi }\theta ^{3}\log^{3}\left ( 2\sin\frac{\theta }{2} \right )\mathrm{d}\theta $
Jan 11, 2017
9
How to prove that $\sum_{k=1}^n\frac{1}{\sqrt[n]{k!} }\sim \frac{n}{\ln n}$
Aug 21, 2018