English

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.

Keywords

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

R2 v1 2026-06-22T02:26:35.931Z