Recursive computation of generalised Zernike polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:312

Article; Proceedings Paper

Area, I.¹  Dimitrov, Dimitar K.²  Godoy, E.³ 

[1] Univ Vigo, EE Telecomunicac, Dept Matemat Aplicada 2, Vigo 36310, Spain

[2] Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[3] Univ Vigo, EE Ind, Dept Matemat Aplicada 2, Campus Lagoas Marcosende, Vigo 36310, Spain

关键词: Generalised Zernike polynomials;    Rodrigues-type formula;    Ordering of Zernike polynomials;    Bivariate orthogonal polynomials;    Hermite-Zernike polynomials;   

DOI  :  10.1016/j.cam.2015.11.017

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free