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We obtain closed expressions for weighted orthogonal polynomials and optimalapproximants associated with the function $f(z)=1-\frac{1}{\sqrt{2}}(z_1+z_2)$and a scale of Hilbert function spaces in the unit $2$-ball having reproducingkernel $(1-\langle z,w\rangle)^{-\gamma}$, $\gamma>0$. Our arguments areelementary but do not rely on reduction to the one-dimensional case.

Optimal approximants and orthogonal polynomials in several variables II: families of polynomials in the unit ball