LaguerrePoly(n)

% LaguerrePoly.m by David Terr, Raytheon, 5-11-04

% Given nonnegative integer n, compute the 
% Laguerre polynomial L_n. Return the result as a vector whose mth
% element is the coefficient of x^(n+1-m).
% polyval(LaguerrePoly(n),x) evaluates L_n(x).


function Lk = LaguerrePoly(n)

if n==0 
    Lk = 1;
elseif n==1
    Lk = [-1 1];
else
    
    Lkm2 = zeros(n+1,1);
    Lkm2(n+1) = 1;
    Lkm1 = zeros(n+1,1);
    Lkm1(n) = -1;
    Lkm1(n+1) = 1;

    for k=2:n
        
        Lk = zeros(n+1,1);

        for e=n-k+1:n
            Lk(e) = (2*k-1)*Lkm1(e) - Lkm1(e+1) + (1-k)*Lkm2(e);
        end
        
        Lk(n+1) = (2*k-1)*Lkm1(n+1) + (1-k)*Lkm2(n+1);
        Lk = Lk/k;
        
        if k<n
            Lkm2 = Lkm1;
            Lkm1 = Lk;
        end
        
    end
    
end