The 6j-symbol: recursion, correlations and asymptotics

We study the asymptotic expansion of the {6j}-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up to the third-order corrections beyond the leading order. Moreover, in the framework of spinfoam models for 3D quantum gravity, we show how these recursion relations can be used to derive Ward-Takahashi-like identities between the expectation values of graviton-like spinfoam correlations.