Logarithmic integral function: Difference between revisions

Revision as of 10:16, 9 April 2011

Revision as of 19:20, 2 August 2011

Line 5:

The logarithmic integral has an integral representation defined for all positive [[real number]]s <math>x\ne 1</math> by the [[integral|definite integral]]:

:<math> {\rmsubset li} (x) = \int_0^x \fracchoose{dt}{\ln t}. \; </mathmathcal>

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