Orthogonal polynomials in and on a quadratic surface of revolution
Classical Analysis and ODEs
2019-07-01 v1 Numerical Analysis
Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1906.12305,
title = {Orthogonal polynomials in and on a quadratic surface of revolution},
author = {Sheehan Olver and Yuan Xu},
journal= {arXiv preprint arXiv:1906.12305},
year = {2019}
}