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questions
11
votes
1
answer
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A cool integral: $\int^{\ln{\phi}}_{0}\ln\left(e^{x}-e^{-x}\right)dx=-\frac{\pi^2}{20}$
I was looking at the equation $\ln{e^{x}-e^{-x}}$ and found that the zero was at $x=\ln{\phi}$ where $\phi$ is the golden ratio. I thought that was pretty cool so I attempted to find the integral. I ...
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3
votes
1
answer
148
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Explicit value of $\operatorname{Li}_2(1/2-{\rm i}/2)$
When you ask Wolfram Alpha about the value of $\operatorname{Li}_{2}\left(1/2-{\rm i}/2\right)$ it gives you $$
\frac{5\pi^{2}}{96} -
\frac{\ln^{2}\left(2\right)}{8} +
{\rm i}\left[\frac{\pi\ln\left(2\...
