Logarithmic integral function: Difference between revisions

Revision as of 21:16, 11 December 2021

Revision as of 14:04, 24 February 2022

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This gives the following more accurate asymptotic behaviour:

:<math> \operatorname{li}(x) - \frac{x}{ \ln x} = O \left( \frac{x}{(\ln^2 x)^2} \right) . </math>

As an asymptotic expansion, this series is [[divergent series|not convergent]]: it is a reasonable approximation only if the series is truncated at a finite number of terms, and only large values of ''x'' are employed. This expansion follows directly from the asymptotic expansion for the [[exponential integral]].