  Orthogonal polynomials and expansions are studied for the weight function
$h_\kappa^2(x) \|x\|^{2\nu} (1-\|x\|^2)^{\mu-1/2}$ on the unit ball of
$\mathbb{R}^d$, where $h_\kappa$ is a reflection invariant function, and for
related weight function on the simplex of $\mathbb{R}^d$. A concise formula for
the reproducing kernels of orthogonal subspaces is derived and used to study
summability of the Fourier orthogonal expansions.
