Artículos de revistas
Recursive computation of generalised Zernike polynomials
Fecha
2017-03-01Registro en:
Journal Of Computational And Applied Mathematics. Amsterdam: Elsevier Science Bv, v. 312, p. 58-64, 2017.
0377-0427
10.1016/j.cam.2015.11.017
WOS:000387297900007
WOS000387297900007.pdf
Autor
Univ Vigo
Universidade Estadual Paulista (Unesp)
Institución
Resumen
An algorithmic approach for generating generalised Zernike polynomials by differential operators and connection matrices is proposed. This is done by introducing a new order of generalised Zernike polynomials such that it collects all the polynomials of the same total degree in a column vector. The connection matrices between these column vectors composed by the generalised Zernike polynomials and a family of polynomials generated by a Rodrigues formula are given explicitly. This yields a Rodrigues type formula for the generalised Zernike polynomials themselves with properly defined differential operators. Another consequence of our approach is the fact that the generalised Zernike polynomials obey a rather simple partial differential equation. We recall also how to define Hermite Zernike polynomials. (C) 2015 Elsevier B.V. All rights reserved.
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