I recently heard from a couple astronomy graduate students that Sundman solved the entire three-body problem of Newtonian gravity over a century ago, for generic initial conditions with non-vanishing angular momentum. This sounds almost too good to be true!
They said the general solution was either a series in powers of $t^{1/3}$ or powers of $\frac{e^{\alpha t^{1/3}} - 1}{e^{\alpha t^{1/3}} + 1}$ for some appropriate $\alpha$, the former related to binary collisions and the latter related to a conformal mapping.
I have briefly searched for discussions of these results of Sundman, but I haven't seen explicit forms for the series and I'm left unsure whether his proof of a series was constructive. My sense is perhaps that the transformations above can be used to argue that such an analytic solution exists but does not give the solution explicitly or a way to find the solution explicitly. However, on e.g. Wikipedia, it's stated that one would need to include truly massive numbers of terms for the series to be of practical value, which makes it sound that the series is explicitly known or can be constructed.
My question is: is Sundman's solution to the three-body problem constructive? If so, what is the series solution in terms of the nine initial positions and nine initial velocities of the bodies? For example, an explicit, iterative way of computing the coefficients in the series would suffice.
