Generalized Zernike or disc polynomials
The paper is devoted to the study of the generalized Zernike or disc polynomials, which are orthogonal 2D polynomials on the unit disc and can be expressed by Jacobi polynomials of transformed arguments. Two differential equations, a first-order and a second-order one with a certain degree of freedom, and the operators of lowering and raising of the indices are derived. Finally, new generating functions are presented by using an operational representation which is alternative to the Rodrigues-type representation.
Rodrigues and operational definitions of disc polynomials
scientific article; zbMATH DE number 2137446
scientific article