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A new and efficient method for the computation of Legendre coefficients
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).Comment: 5 page
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