  We revisit the problem of three identical bosons in free space, which
exhibits a universal hierarchy of bound states (Efimov trimers). Modelling a
narrow Feshbach resonance within a two-channel description, we map the integral
equation for the three-body scattering amplitude to a one-dimensional
Schr\"odinger-type single-particle equation, where an analytical solution of
exponential accuracy is obtained. We give exact results for the trimer binding
energies, the three-body parameter, the threshold to the three-atom continuum,
and the recombination rate.
