Wigner d and D matrices using the exact diagonalization algorithm of Feng (2015), following the phase convention of Varshalovich et al. (1988).
julia> wignerd(0.5, 0)
2×2 Matrix{Float64}:
1.0 -0.0
0.0 1.0
julia> wignerd(1, pi/3)
3×3 Matrix{Float64}:
0.75 0.612372 0.25
-0.612372 0.5 0.612372
0.25 -0.612372 0.75
julia> WignerD.wignerdjmn(1, 1, 1, pi/3)
0.7500000000000004
julia> wignerD(1, 0, pi/3, pi/2)
3×3 Matrix{ComplexF64}:
4.59243e-17+0.75im 0.612372-0.0im 1.53081e-17-0.25im
-3.7497e-17-0.612372im 0.5+0.0im 3.7497e-17-0.612372im
1.53081e-17+0.25im -0.612372+0.0im 4.59243e-17-0.75im
julia> WignerD.wignerDjmn(1, 1, 1, 0, pi/3, pi/2)
4.592425496802577e-17 - 0.7500000000000004im