Since MTEX version 5.9 we use L2 normalized Wigner-D functions as basis functions for the harmonic series expansion of ODFs/SO3Funs.
Up to MTEX version 5.8 the ODFs has been definded by \[ F({\bf R}) = \sum \hat{f}_n^{k,l} \, D_n^{k,l}({\bf R})\] with \( D_n^{k,l}({\bf R}(\alpha,\beta,\gamma)) = \mathrm e^{-\mathrm i k\gamma} \mathrm d_n^{k,l}(\cos\beta) \,e^{-\mathrm i l\alpha} \). Hence the \(L_2\) norm of the Wigner-D function \(D_n^{k,l}\) was \(\sqrt{2n+1}\).
Now since MTEX version 5.9 the Wigner-D functions have \(L_2\) norm 1. Hence they are defined by \( D_n^{k,l}({\bf R}(\alpha,\beta,\gamma)) = \sqrt{2n+1} \, \mathrm e^{-\mathrm i k\gamma} \mathrm d_n^{k,l}(\cos\beta) \, e^{-\mathrm i l\alpha} \).
Take a look at Wigner-D functions.
Syntax
SO3F = L2normalizeFourierCoefficients(SO3F)