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x_x [2016/04/05 09:30] nikolaj |
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| == Representations == | == Representations == | ||
| - | ^ $x^x={\mathrm e}^{x\log(x)}$ ^ | + | ^ $x^x={\mathrm e}^{x\log(x)}=\left({\mathrm e}^x\right)^{\log(x)}$ ^ |
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| + | >todo: write down the above with an expanded $\log$ to third order | ||
| Because of this, the local minimum of $x^x$ is that of $x\log(x)$, namely $\frac{1}{\mathrm e}\approx 0.37$, and then see | Because of this, the local minimum of $x^x$ is that of $x\log(x)$, namely $\frac{1}{\mathrm e}\approx 0.37$, and then see | ||
