# Generalized Zernike polynomials: operational formulae and generating functions

@article{Aharmim2013GeneralizedZP, title={Generalized Zernike polynomials: operational formulae and generating functions}, author={Bouchra Aharmim and El Hamyani Amal and El Wassouli Fouzia and Allal Ghanmi}, journal={Integral Transforms and Special Functions}, year={2013}, volume={26}, pages={395 - 410} }

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.

## 2 Citations

### Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2018

Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue. The resulting…

### Orthogonal Polynomial Projection Error Measured in Sobolev Norms in the Unit Disk

- MathematicsConstructive Approximation
- 2016

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