Hermite polynomials on the plane PDF
8 Pages·2007·0.241 MB·English
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The space {\cal P}_n of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for {\cal P}_n which consists of the rotations of a single polynomial through the angles {\ell\pi\over n+1} , ℓ=0,...n. Thus we obtain an orthogonal expansion which retains as much of the symmetry of {\cal P}_n as is possible. Indeed we show that a continuous version of this orthogonal expansion exists.
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