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).
- Pub Date:
- June 2011
- Mathematics - Numerical Analysis;
- Mathematical Physics;
- 5 pages