A new and efficient method for the computation of Legendre coefficients
Abstract
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 Abeltype 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 Abeltype transform of f(x).
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 DOI:
 10.48550/arXiv.1106.0463
 arXiv:
 arXiv:1106.0463
 Bibcode:
 2011arXiv1106.0463D
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematical Physics;
 42C10;
 65T50
 EPrint:
 5 pages