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Machinato
  • Member for 9 years, 2 months
  • Last seen more than a month ago
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About

Random PhD student in Random geometry at Charles Uni Prague. About me & my research (podcast in Czech: here)

My faculty webpage (with contact info:) https://www.karlin.mff.cuni.cz/~beckd/

Do not disturb my circles!

original contributions (listed by own intervention) :

  1. new elementary aproach to Gaussian integral $\int_{0}^{\infty}e^{-x^2}\mathrm{d}x$
  2. another proof of $\sum_{n=1}^{\infty}\frac1{n^3}\frac{\sinh\pi n\sqrt2-\sin\pi n\sqrt2}{{\cosh\pi n\sqrt2}-\cos\pi n\sqrt2}=\frac{\pi^3}{18\sqrt2}$, by the same argument $\sum_{n = 1}^{\infty}\{\coth (n\pi x) + x^{2}\coth(n\pi/x)\}/n^{3}$ is found in closed form
  3. simpler proof of $ \int_{-1}^{1} \frac{1}{x} \sqrt{\frac{1+x}{1-x}} \ln \left(\frac{2x^2+2x+1}{2x^2-2x+1}\right) \,\mathrm{d}x = 4\pi\operatorname{arccot}\sqrt{\phi}$

Life is great art gallery of beauty

0.207879576...

Logarithmic spiral

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