Difference between revisions of "Logarithmic integral"
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(Created page with "The logarithmic integral is $$\mathrm{li}(x) = \displaystyle\int_0^x \dfrac{dt}{\log(t)},$$ where $\log$ denotes the logarithm. It can be shown that $\mathrm{li}(x)=\mathr...") |
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The logarithmic integral is | The logarithmic integral is | ||
$$\mathrm{li}(x) = \displaystyle\int_0^x \dfrac{dt}{\log(t)},$$ | $$\mathrm{li}(x) = \displaystyle\int_0^x \dfrac{dt}{\log(t)},$$ | ||
| − | where $\log$ denotes the [[logarithm]]. | + | where $\log$ denotes the [[logarithm]]. The logarithmic integral is related to the [[exponential integral]] by the formula |
| + | $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)).$$ | ||
Revision as of 20:57, 4 October 2014
The logarithmic integral is $$\mathrm{li}(x) = \displaystyle\int_0^x \dfrac{dt}{\log(t)},$$ where $\log$ denotes the logarithm. The logarithmic integral is related to the exponential integral by the formula $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)).$$
