Generalized Zernike polynomials: Operational formulae and generating functions
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.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 DOI:
 10.48550/arXiv.1312.3628
 arXiv:
 arXiv:1312.3628
 Bibcode:
 2013arXiv1312.3628A
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematical Physics;
 33C45;
 42C05;
 58C40
 EPrint:
 16 pages