## Encyclopedia > Offset logarithmic integral

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# Offset logarithmic integral

The offset logarithmic integral is a non-elementary function Li(x) very similar to the logarithmic integral function li(x), defined such that:

Li(x) = li(x) - li(2).

Explicitly, this means

${\rm Li} (x) = \int_{2}^{x} \frac{dt}{\ln (t)} \; .$

It is often used in formulations of the prime number theorem.

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