A new and efficient method for the computation of Legendre coefficients

Details A new and efficient method for the computation of Legendre coefficients A new and efficient method for the computation of Legendre coefficients

2011-06-02

arxiv.org/abs/1106.0463v1

Mathematics

Numerical Analysis

5 pages

Scientific paper

An efficient procedure for the computation of the coefficients of Legendre expansions is here presented. We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of an Abel-type transform of f(x). The computation of N Legendre coefficients can then be performed in O(N log N) operations with a single Fast Fourier Transform of the Abel-type transform of f(x).

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