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arXiv · 2509.19225

Chebyshev Expansion of the Zernike Polynomials

Richard J. Mathar
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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. 2025-11-20. Chebyshev Expansion of the Zernike Polynomials. https://arxiv.org/abs/2509.19225

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