Chebyshev Expansion of the Zernike Polynomials
arXiv:2509.19225
Abstract
The even and odd Zernike Polynomials R_n^m(x) can be expanded into sums of even and odd Chebyshev Polynomials T_i(x). This manuscript provides closed forms for the rational expansion coefficients c_{n,m,i} for a set of small 0 <= n-m <= 6 and a holonomic five-term recurrence for these coefficients for all larger n.
Version 2 includes 5-term recurrences also for Zernike Functions in higher dimensions