A new and efficient method for the computation of Legendre coefficients
Enrico De Micheli, G. A. Viano · arXiv (Cornell University) · 2011
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).