Pushing the asymptotics of the 6j-symbol further

In the context of spin-foam models for quantum gravity, we investigate the asymptotical behavior of the (6j)-symbol at next-to-leading order. This gives the first quantum gravity correction to the (3d) Regge action. We compute it analytically and check our results against numerical calculations. The (6j)-symbol is the building block of the Ponzano-Regge amplitudes for 3d quantum gravity, and the present analysis is directly relevant to deriving the quantum corrections to gravitational correlations in the spin-foam formalism.