This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 LegendreP LegendreP[n, x] gives the Legendre polynomial . LegendreP[n, m, x] gives the associated Legendre polynomial . Mathematical function (see Section A.3.10). Explicit formulas are given for integer n and m. The Legendre polynomials satisfy the differential equation . The Legendre polynomials are orthogonal with unit weight function. The associated Legendre polynomials are defined by . For arbitrary complex values of n, m and z, LegendreP[n, z] and LegendreP[n, m, z] give Legendre functions of the first kind. LegendreP[n, m, a, z] gives Legendre functions of type a. The default is type 1. The symbolic form of type 1 involves , of type 2 involves and of type 3 involves . Type 1 is defined only for within the unit circle in the complex plane. Type 2 represents an analytic continuation of type 1 outside the unit circle. Type 2 functions have branch cuts from to and from to in the complex plane. Type 3 functions have a single branch cut from to . LegendreP[n, m, a, z] is defined to be Hypergeometric2F1Regularized[-n,n+1,1-m,(1-z)/2] multiplied by for type 2 and by for type 3. See Section 3.2.9 and Section 3.2.10. See also: SphericalHarmonicY. New in Version 1; modified in 5.0.