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offset_logarithmic_integral [2014/02/25 23:59] nikolaj |
offset_logarithmic_integral [2014/02/26 00:03] nikolaj |
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| | @#FFBB00: $ \mathrm{Li}: \mathbb R_+\to \mathbb R_+$ | | | @#FFBB00: $ \mathrm{Li}: \mathbb R_+\to \mathbb R_+$ | | ||
| | @#FFBB00: $ \mathrm{Li}(x) := \mathrm{li}(x)-\mathrm{li}(2) $ | | | @#FFBB00: $ \mathrm{Li}(x) := \mathrm{li}(x)-\mathrm{li}(2) $ | | ||
| - | |||
| - | I.e. $ \mathrm{li}(x) := \int_0^x \frac{1}{\ln(t)}\mathrm d t $ | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | === Alternative definition === | ||
| + | $ \mathrm{Li}(x) := \int_2^x \frac{1}{\ln(t)}\mathrm d t $ | ||
| + | === Theorems === | ||
| + | $ \mathrm{Li}(x)\approx\pi(x) $ | ||
| + | >todo: [[Prime counting-function]] | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Logarithmic_integral_function|Logarithmic integral function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Logarithmic_integral_function|Logarithmic integral function]] | ||
