Recursive computation of generalised Zernike polynomials - Area, I.; Dimitrov, Dimitar K. [UNESP]; Godoy, E. (Elsevier B.V., 2017)
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.
Keywords: Generalised Zernike polynomials; Rodrigues-type formula; Ordering of Zernike polynomials; Bivariate orthogonal polynomials; Hermite-Zernike polynomials