CentralNotice Legendre polynomials From Wikipedia, the free encyclopedia Jump to: navigation , search For Legendre's Diophantine equation, see Legendre's equation . Associated Legendre polynomials are the most general solution to Legendre's Equation and Legendre polynomials are solutions that are azimuthally symmetric. In mathematics , Legendre functions are solutions to Legendre's differential equation : ( 1 ) They are named after Adrien-Marie Legendre . This ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations ) in spherical coordinates . The Legendre differential equation may be solved using the standard power series method. The equation has regular singular points at x = ±1 so, in gene...