Papers › Orthogonal polynomials in and on a quadratic surface of revolution
Orthogonal polynomials in and on a quadratic surface of revolution
Sheehan Olver, Yuan Xu
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We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizing spherical harmonics to the surface of a cone, hyperboloid, and paraboloid. We use this construction to develop cubature and fast approximation methods.
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