I am trying to find the expectation of a relatively simple expression under a lognormal distribution with mean [Mu] - [Sigma]^2/2 and variance [Sigma]^2 , but it hangs for a long while and eventually returns the original question:
In:= Expectation[(2 Sqrt[x])/(x + 1) - 1, x \[Distributed] LogNormalDistribution[ (\[Mu] - \[Sigma]^2/2), \[Sigma]]] Out= Expectation[-1 + (2 Sqrt[x])/(1 + x), x \[Distributed] LogNormalDistribution[\[Mu] - \[Sigma]^2/2, \[Sigma]]]
I have tried putting an Abs around the Sqrt to only take the positive root just in case that was the issue, without success. I have also tried adding Assumptions to the effect that x>0, [Sigma] > 0 but that made no difference.
Any pointers greatly appreciated!