Cerjan Charles
Lawrence Livermore National Laboratory, Livermore California 94550, USA.
J Phys Chem A. 2006 Apr 27;110(16):5495-8. doi: 10.1021/jp056468b.
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 decaying functions or functions with finite support.
