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 offset_logarithmic_integral [2014/02/26 00:01]nikolaj offset_logarithmic_integral [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2014/02/26 00:03 nikolaj 2014/02/26 00:01 nikolaj 2014/02/25 23:59 nikolaj 2014/02/25 23:59 nikolaj 2014/02/25 23:59 nikolaj 2014/02/25 23:58 nikolaj created Next revision Previous revision 2014/02/26 00:03 nikolaj 2014/02/26 00:01 nikolaj 2014/02/25 23:59 nikolaj 2014/02/25 23:59 nikolaj 2014/02/25 23:59 nikolaj 2014/02/25 23:58 nikolaj created Line 1: Line 1: ===== 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 === $\mathrm{Li}(x)\approx\pi(x)$ $\mathrm{Li}(x)\approx\pi(x)$ >todo: [[Prime counting-function]] >todo: [[Prime counting-function]]