Bessel-zernike discrete variable representation basis.

@article{Cerjan2006BesselzernikeDV,
  title={Bessel-zernike discrete variable representation basis.},
  author={Charles J Cerjan},
  journal={The journal of physical chemistry. A},
  year={2006},
  volume={110 16},
  pages={5495-8}
}
The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the unit interval. Expressing a Bessel function in a Zernike expansion provides a straightforward method of generating series identities. Furthermore, the Zernike polynomials may also be used to efficiently evaluate the Hankel transform for rapidly… CONTINUE READING