Classes Of Bivariate Orthogonal Polynomials

Keywords

2D-Jacobi polynomials; 2D-Laguerre polynomials; Biorthogonal functions; Connection relations; Disc polynomials; Generating functions; Generating functions; Ladder operators; Q-2D-Jacobi polynomials; Q-2D-La-guerre polynomials; Q-integrals; Q-Sturm-Liouville equations; Q-Zernike polynomials; Rodrigues formulas; Zernike polynomials; Zeros

Abstract

We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-D Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-D Hermite polynomials and a two variable extension of the Zernike or disc polynomials. We also give q-analogues of all these extensions. In each case in addition to generating functions and three term recursions we provide raising and lowering operators and show that the polynomials are eigenfunctions of second-order partial differential or q-difference operators.

Publication Date

2-24-2016

Publication Title

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Volume

12

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.3842/SIGMA.2016.021

Socpus ID

84959199347 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84959199347

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