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offset_logarithmic_integral [2014/02/25 23:59] nikolaj |
offset_logarithmic_integral [2014/03/21 11:11] (current) |
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| ===== Offset logarithmic integral ===== | ===== Offset logarithmic integral ===== | ||
| ==== Function ==== | ==== Function ==== | ||
| - | | @#FFBB00: $ \mathrm{Li}: \mathbb R_+\to \mathbb R_+$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \mathrm{Li}: \mathbb R_+\to \mathbb R_+$ | |
| - | | @#FFBB00: $ \mathrm{Li}(x) := \mathrm{li}(x)-\mathrm{li}(2) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \mathrm{Li}(x) := \mathrm{li}(x)-\mathrm{li}(2) $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Alternative definition === | === Alternative definition === | ||
| $ \mathrm{Li}(x) := \int_2^x \frac{1}{\ln(t)}\mathrm d t $ | $ \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]] | ||
