Weighted Sobolev orthogonal polynomials on the unit ball

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For the weight function Wμ(x) = (1-|x|²)μ, μ> -1, λ> 0 and bμ a normalizing constant, a family of mutually orthogonal polynomials on the unit ball with respect to the inner product f,g = bμ[∫ᵈ f(x) g(x) Wμ(x) dx + λ∫ᵈ ∇ f(x) · ∇ g(x) Wμ(x) dx] are constructed in terms of spherical harmonics and a sequence of Sobolev orthog onal polynomials of one variable. The latter ones, hence, the orthogonal polynomials with respect to ·,·, can be generated through a recursive formula.