Fourier-Legendre series

Fourier-Legendre series

[‚fu̇r·ē‚ā lə′zhän·drə ‚sir·ēz]
(mathematics)
Given a function ƒ(x), the series from n = 0 to infinity of an Pn (x), where Pn (x), n =0, 1, 2, …, are the Legendre polynomials, and an is the product of (2 n + 1)/2 and the integral over x from -1 to 1 of ƒ(x) Pn (x).