Generalized Zernike polynomials: Operational formulae and generating functions
Classical Analysis and ODEs
2015-04-03 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1312.3628,
title = {Generalized Zernike polynomials: Operational formulae and generating functions},
author = {Bouchra Aharmim and Amal El Hamyani and Fouzia El Wassouli and Allal Ghanmi},
journal= {arXiv preprint arXiv:1312.3628},
year = {2015}
}
Comments
16 pages