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arXiv · 1106.4718

The expansion in ultraspherical polynomials: a simple procedure for the fast computation of the ultraspherical coefficients

Enrico De Micheli·Giovanni Alberto Viano
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Abstract

We present a simple and fast algorithm for the computation of the coefficients of the expansion of a function f(cos u) in ultraspherical (Gegenbauer) polynomials. We prove that these coefficients coincide with the Fourier coefficients of an Abel-type transform of the function f(cos u). This allows us to fully exploit the computational efficiency of the Fast Fourier Transform, computing the first N ultraspherical coefficients in just O (N log_2 N) operations.

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Enrico De Micheli, Giovanni Alberto Viano. 2011-06-23. The expansion in ultraspherical polynomials: a simple procedure for the fast computation of the ultraspherical coefficients. https://arxiv.org/abs/1106.4718

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