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offset logarithmic integral |
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:<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>
Sometimes instead of li the [[offset logarithmic integral]] is used, defined as
<math>{\rm Li}(x) = {\rm li}(x) - {\rm li}(2)</math>. This is often used in number theoretic applications.
The growth behavior of this function for ''x'' → ∞ is
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