# Inverse functions - how are they calculated?

Mathematica is able to calculate InverseFunction[LogIntegral] and InverseFunction[RiemannR] (and many other inverse functions). How are these calculated? (I can see how LogIntegral and RiemannR are calculated if I go to the details section of the docs, but can't find a ref. for inverse functions.)

Note: I have tried looking at Series[LogIntegral[n], {n, 2, 3}], and InverseSeries[Series[LogIntegral[n], {n, 2, 3}]], but can't see clearly how this helps.

• I believe it uses numerical inversion in some cases. InverseFunction[LogIntegral][1] gives a Root object in v9 which suggests it uses the technology described here. May 21 '14 at 14:17
• Great - thank you :) May 21 '14 at 14:24

Trace[InverseFunction[LogIntegral], TraceInternal -> True]