Point-to-ellipse Fourier series

2025/06/18 by John-Olof Nilsson, Nilsson, John-Olof
Mathematics · #42A16 #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2507.08807

openalex publication_date 2025/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fourier series with power series coefficients for the normal and distance to a point from an ellipse are derived. These expressions are the first of their kind and opens up a range of analysis and computational possibilities.

Citations

• Minimax polynomial ECEF to geodetic coordinate transformation approximations
• A comprehensive Cartesian to geodetic coordinate transformation reference listing
• A fast algorithm for computing Bell polynomials based on index\n break-downs using prime factorization

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• A primer on Fourier Series
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• Fourier Analysis: A New Result