Beta mixture approximations

For \(\mathcal D = [0, 1]\), the beta basis functions are given by

\[ \ell_m(t) = b_m t^m (1 - t)^{M - m}, \qquad b_m = \frac{(M+1)!}{m! (M-m)!}, \]

where \(b_m\) is a normalization constant. These basis functions do not contain any hyperparameters.