Logarithmic integral function: Difference between revisions

Revision as of 16:12, 11 March 2018

Revision as of 18:29, 15 March 2018

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Here, {{math|ln}} denotes the [[natural logarithm]]. The function {{math|1/ln(''t'')}} has a [[mathematical singularity|singularity]] at {{mvar|t}} = 1, and the integral for {{mvar|x}} > 1 has to be interpreted as a ''[[Cauchy principal value]]'',

:<math> {\rm li} (x) = \lim_{\varepsilon \to 0+} \left( \int_0^{1-\varepsilon} \frac{dt}{\ln t} + \int_{1+-\varepsilon}^x \frac{dt}{\ln t} \right)~.</math>

==Offset logarithmic integral==