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x_x [2016/04/05 09:29] nikolaj |
x_x [2016/04/05 09:30] nikolaj |
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| >this must come from the Expression at the beginning, but I don't know how I arrived there. | >this must come from the Expression at the beginning, but I don't know how I arrived there. | ||
| - | >Maybe I also switched from $\int_0^1$ to $\int_1^0$. | + | >Maybe there I switched from $x$ to $1-x$ or $\int_0^1$ to $\int_1^0$. |
| $\int_0^1 \, x^x \, dx = \sum_{n=0}^\infty \frac{1}{n!} \int_0^1 \, P_n(x) \, dx = \frac{1}{2} + \frac{1}{12} + \frac{1}{24} + \frac{131}{5040} + \frac{1093}{60480} + \dots$ | $\int_0^1 \, x^x \, dx = \sum_{n=0}^\infty \frac{1}{n!} \int_0^1 \, P_n(x) \, dx = \frac{1}{2} + \frac{1}{12} + \frac{1}{24} + \frac{131}{5040} + \frac{1093}{60480} + \dots$ | ||
