Chebyshev Expansion of the Zernike Polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909915257241600 |
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| author | Mathar, Richard J. |
| author_facet | Mathar, Richard J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chebyshev Expansion of the Zernike Polynomials Mathar, Richard J. Classical Analysis and ODEs 26C05 (Primary) 42C05, 33C20 (Secondary) J.2; I.1.2; G.4 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. |
| title | Chebyshev Expansion of the Zernike Polynomials |
| topic | Classical Analysis and ODEs 26C05 (Primary) 42C05, 33C20 (Secondary) J.2; I.1.2; G.4 |
| url | https://arxiv.org/abs/2509.19225 |