Recursive computation of generalised Zernike polynomials

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• 作者：I. Area^a ; ^{area@uvigo.es" class="auth_mail" title="E-mail the corresponding author} ; Dimitar K. Dimitrov^b ; ^{dimitrov@ibilce.unesp.br" class="auth_mail" title="E-mail the corresponding author} ; E. Godoy^c ; ^{egodoy@dma.uvigo.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：41A21 ; 41A27 ; 37K10 ; 47N20 ; 42C05 ; 33D45 ; 39A13
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：58-64
• 全文大小：388 K

文摘

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.