Chebyshev Expansion of the Zernike Polynomials

Published 23 Sep 2025 in math.CA | (2509.19225v1)

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.

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Richard J. Mathar

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