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Mathematics
Vivek Kaushik's user avatar
Vivek Kaushik's user avatar
Vivek Kaushik's user avatar
Vivek Kaushik
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Mathematics Ph.D. Student at University of Illinois Urbana Champaign.

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answer
21
Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$
Sep 19, 2019
question
19
A Challenging Integral: $\int_{0}^{1} \frac{x \arcsin(x/2) \log(x)}{x^2-1} \ dx=\frac{5 \pi^3}{1296}$
Feb 13, 2019
answer
19
Prove $\int_{0}^{\infty}\frac{2x}{x^8+2x^4+1}dx=\frac{\pi}{4}$
May 30, 2016
answer
17
Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?
May 22, 2016
answer
11
Quadruple Integral $\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\frac1{1-xyzw}\,dw\,dz\,dy\,dx$
Jun 28, 2017
answer
10
Different ways to prove $\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$ (the Basel problem)
Aug 13, 2015
answer
10
Evaluation of Gaussian integral $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx$
Aug 13, 2015
answer
9
Does $\int_{0}^1\frac{\ln(1+x+x^2)}{x}\mathrm dx$ have a closed form?
May 28, 2016
answer
9
Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$
Jul 8, 2016
answer
8
Prove $\lim_{x\to 1} \frac{x+2}{x^2+1}=\frac{3}{2}$
Sep 10, 2017