Point-to-ellipse Fourier series
John-Olof Nilsson
TL;DR
This paper introduces novel Fourier series expressions with power series coefficients for an ellipse, enabling new analytical and computational methods for geometric analysis.
Contribution
It derives the first Fourier series formulas with power series coefficients for the normal and distance from a point to an ellipse.
Findings
Provides the first such Fourier series formulas for ellipses.
Enables new analysis and computational techniques for elliptical geometries.
Lays groundwork for further research in geometric Fourier analysis.
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.
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Taxonomy
TopicsMathematical functions and polynomials · Differential Equations and Boundary Problems · Algebraic and Geometric Analysis