Some Properties of the Fractional Circle Zernike Polynomials

Abstract

In this paper, we present a fractional extension of the classical circle Zernike polynomials defined via g-Jacobi functions. Some properties of this new class of functions are studied, such as recurrence relations for consecutive and distant neighborhoods, and differential relations. A graphic representation for the proposed fractional circle Zernike polynomials will be presented in the final section of the paper.