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Mathematics
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SSS
  • Member for 5 years, 4 months
  • Last seen more than a month ago
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59
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29
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question
7
Showing $\int_0^\infty\frac{Li_2\frac{(1-x^4)^2}{(1+x^4)^2}}{1+x^4}dx=\sqrt2\,\Re\left(\int_0^1\frac{Li_2\frac{(1+x^4)^2}{(1-x^4)^2}}{1+x^2}dx\right)$
Sep 6, 2021
answer
5
Different ways to prove $\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$ (the Basel problem)
Dec 23, 2020
answer
5
Showing $\int_0^\infty\frac{Li_2\frac{(1-x^4)^2}{(1+x^4)^2}}{1+x^4}dx=\sqrt2\,\Re\left(\int_0^1\frac{Li_2\frac{(1+x^4)^2}{(1-x^4)^2}}{1+x^2}dx\right)$
Sep 11, 2021
answer
4
$\int_0^{\pi/2} e^{-\tan^2(x)}\,dx=\frac{\pi e}{2}\big(1-\operatorname{erf}(1)\big)$
Sep 8, 2021
answer
4
Why is $\cos(-x)$ always $\cos(x)$?
Sep 12, 2021
answer
3
Many terms has appeared as I try to derive $~ \lim_{ x \to \infty} \left( \sqrt{ x^2+a^2 } -x \right) =0 ~$
Sep 8, 2021
question
2
Challenge: $\int_0^\infty\frac1{1+x}\ln\left(\prod_{k=0}^\infty(1+e^{-(2k+1)\sqrt{x}})(1+e^{-(2k+1)\pi^2\sqrt{x}})\right)\,dx=\pi^3/24+\pi/24-\ln^22$
Sep 21, 2023
question
2
How to compute poly-Hurwitz zeta function??
Feb 23
answer
2
Challenging Integral: $\int_0^\infty\frac{\ln(2+x)\operatorname{Li}_2(-x)}{x(2+x)}dx$
Aug 19, 2020
answer
2
Evaluating the integral $ \int_0^1 \frac{e^{-y^2(1+v^2)}}{(1+v^2)^n}dv$
Sep 8, 2021