Fancy Matlab

>> help legendre

 LEGENDRE Associated Legendre function.
    P = LEGENDRE(N,X) computes the associated Legendre functions
    of degree N and order M = 0, 1, ..., N, evaluated for each element
    of X.  N must be a scalar integer and X must contain real values
    between -1 <= X <= 1.

    If X is a vector, P is an (N+1)-by-L matrix, where L = length(X).
    The P(M+1,i) entry corresponds to the associated Legendre function
    of degree N and order M evaluated at X(i).

    In general, the returned array has one more dimension than X.
    Each element P(M+1,i,j,k,...) contains the associated Legendre
    function of degree N and order M evaluated at X(i,j,k,...).

    There are three possible normalizations, LEGENDRE(N,X,normalize)
    where normalize is 'unnorm','sch' or 'norm'.

    The default, unnormalized associated Legendre functions are:

        P(N,M;X) = (-1)^M * (1-X^2)^(M/2) * (d/dX)^M { P(N,X) },

    where P(N,X) is the Legendre polynomial of degree N. Note that
    the first row of P is the Legendre polynomial evaluated at X
    (the M == 0 case).

    SP = LEGENDRE(N,X,'sch') computes the Schmidt semi-normalized
    associated Legendre functions SP(N,M;X). These functions are
    related to the unnormalized associated Legendre functions
    P(N,M;X) by:

    SP(N,M;X) = P(N,X), M = 0
              = (-1)^M * sqrt(2*(N-M)!/(N+M)!) * P(N,M;X), M > 0

    NP = LEGENDRE(N,X,'norm') computes the fully-normalized
    associated Legendre functions NP(N,M;X). These functions are
    normalized such that

             /1
            |
            | [NP(N,M;X)]^2 dX = 1    ,
            |
            /-1

    and are related to the unnormalized associated Legendre
    functions P(N,M;X) by:

    NP(N,M;X) = (-1)^M * sqrt((N+1/2)*(N-M)!/(N+M)!) * P(N,M;X)

    Examples:
      1. legendre(2, 0.0:0.1:0.2) returns the matrix:

               |    x = 0           x = 0.1         x = 0.2
         ------|---------------------------------------------
         m = 0 |   -0.5000         -0.4850         -0.4400
         m = 1 |         0         -0.2985         -0.5879
         m = 2 |    3.0000          2.9700          2.8800

      2. X = rand(2,4,5); N = 2;
         P = legendre(N,X);

      so that size(P) is 3x2x4x5 and
      P(:,1,2,3) is the same as legendre(N,X(1,2,3)).

# posted by samuel @ 6:27 PM