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How can I get the inverse function of $\operatorname{li}(x)$ over $x>\mu$?

Where $$\operatorname{li}(x)=\int_{0}^{x}\frac{ds}{\ln(s)}$$ is the so-called logarithmic integral, and $\operatorname{li}(\mu)=0$.

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    $\mu$ here is the [Ramanujan-Soldner constant](http://mathworld.wolfram.com/SoldnersConstant.html).2011-12-29
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    $\mathrm{li}(z)=\mathrm{Ei}(\ln\,z)$; your problem here is computing the inverse of the exponential integral.2011-12-29
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    Thanks but I don't understand clearly. How can I compute the inverse of the exponential integral? is it some numerical way?2011-12-29
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    That's the problem. I don't see an easy way to derive a nice approximation for the exponential integral's inverse.2011-12-29

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