Iraqi Ministry of Education, Dhi Qar Education Directorate, Research and Studies Department
10.22080/cjms.2024.27564.1707
Abstract
Zernike circle polynomials use for wavefront analysis because of their orthogonality over a circular. So far, different representations have been presented for these polynomials. In this paper, we introduce Zernike polynomials and their important properties. Also, we present some other orthogonal polynomials such as Bessel functions, Legendre polynomials and Jaccobi polynomials and give some important results of them. Finally, we express the relationship between Zernike orthogonal polynomials and these well-known orthogonal polynomials. For different cases, the radial polynomials in the Zernike functions are obtained using the well-known orthogonal polynomials. These relations frequently used for representing wavefront aberrations.
Al-Tamimi, K. (2024). A relation between Zernike polynomials and other orthogonal polynomials: A review. Caspian Journal of Mathematical Sciences, 13(2), 386-400. doi: 10.22080/cjms.2024.27564.1707
MLA
Kamel Al-Tamimi. "A relation between Zernike polynomials and other orthogonal polynomials: A review", Caspian Journal of Mathematical Sciences, 13, 2, 2024, 386-400. doi: 10.22080/cjms.2024.27564.1707
HARVARD
Al-Tamimi, K. (2024). 'A relation between Zernike polynomials and other orthogonal polynomials: A review', Caspian Journal of Mathematical Sciences, 13(2), pp. 386-400. doi: 10.22080/cjms.2024.27564.1707
CHICAGO
K. Al-Tamimi, "A relation between Zernike polynomials and other orthogonal polynomials: A review," Caspian Journal of Mathematical Sciences, 13 2 (2024): 386-400, doi: 10.22080/cjms.2024.27564.1707
VANCOUVER
Al-Tamimi, K. A relation between Zernike polynomials and other orthogonal polynomials: A review. Caspian Journal of Mathematical Sciences, 2024; 13(2): 386-400. doi: 10.22080/cjms.2024.27564.1707
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