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Orthogonal polynomials and cubature formulae on spheres and on simplices

Orthogonal polynomials and cubature formulae on spheres and on simplices

Orthogonal polynomials on the standard simplex E d in R d are shown to be related to the spherical orthogonal polynomials on the unit sphere S d in R d+1 that are invariant under the group Z2 x • • • x Z2.For a large class of measures on S …