Dilogarithm Identities Is there a cleaner way to write:
$$
f(x) = \operatorname{Li}_2(i x) - \operatorname{Li}_2(-i x)
$$
in terms of simpler functions? I don't know enough about dilogarithms, and the basic identities I see on wikipedia are not helping me.

I can show you some approximations which might help: 
For the case of $|x|<1$ we have that 
$ i(\operatorname{Li}_2(-i x) - \operatorname{Li}_2(i x)) ≃ 2x $
For the case of $|x|\ge1$ we have that 
$ i(\operatorname{Li}_2(-i x) - \operatorname{Li}_2(i x)) ≃ π\cdot log(x) $
Another good approximation for any x is
$ i(\operatorname{Li}_2(-i x) - \operatorname{Li}_2(i x)) ≃ π \cdot arcsinh(x/2) $
