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The Wigner $3j$ symbols of the quantum angular momentum theory are related tothe vector coupling or Clebsch-Gordan coefficients and to the Hahn and dualHahn polynomials of the discrete orthogonal hyperspherical family, of use indiscretization approximations. We point out the important role of the Reggesymmetries for defining the screen where images of the coefficients areprojected, and for discussing their asymptotic properties and semiclassicalbehavior. Recursion relationships are formulated as eigenvalue equations, andexploited both for computational purposes and for physical interpretations.

The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior