Zernike Basis to Cartesian Transformations

@article{Mathar2008ZernikeBT,
  title={Zernike Basis to Cartesian Transformations},
  author={Richard J. Mathar},
  journal={arXiv: Mathematical Physics},
  year={2008}
}
  • R. Mathar
  • Published 13 September 2008
  • Mathematics
  • arXiv: Mathematical Physics
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They may play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by… 
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