Bilateral and Bilinear Generating Functions for the Generalized Zernike or Disc Polynomials

Abstract

In this paper, we obtain some generating functions for the generalized Zernike or disk polynomials \(P_{m,n}^\alpha (z,z^*)\) which are investigated by Wiinsche [13]. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results presented in this study are indicated. Also, it is possible to obtain multilinear and multilateral generating functions for the polynomials \(P_{m,n}^\alpha (z,z^*)\).