Logarithmic integral function: Difference between revisions

Revision as of 15:37, 9 March 2010

Revision as of 11:05, 26 April 2010

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Here, ln denotes the [[natural logarithm]]. The function 1/ln (''t'') has a [[mathematical singularity|singularity]] at ''t'' = 1, and the integral for ''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==