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arXiv · 1312.3628

Generalized Zernike polynomials: Operational formulae and generating functions

Bouchra Aharmim·Amal El Hamyani·Fouzia El Wassouli·Allal Ghanmi
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Abstract

We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish recurrence relations with respect to the argument and the integer indices, as well as Nielsen identities and Runge addition formula. In addition, various new generating functions for these disk polynomials are proved.

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Bouchra Aharmim, Amal El Hamyani, Fouzia El Wassouli, Allal Ghanmi. 2015-04-02. Generalized Zernike polynomials: Operational formulae and generating functions. https://doi.org/10.1080/10652469.2015.1012510

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