In mathematics, Legendre functions are solutions to Legendre‘s differential equation:
In particular, it occurs when solving Laplace‘s equation (and relatedpartial differential equations) in spherical coordinates.
The polynomials may be denoted by Pn(x) , called the Legendre polynomial of order n. The polynomials are either even or odd functions of x for even or odd orders n. The first few polynomials are shown below.
The general form of a Legendre polynomial of order n is given by the sum:
From the Legendre polynomials can be generated another important class of functions for physical problems, the associated Legendre functions.
原文：http://www.cnblogs.com/hiramlee0534/p/5539709.html