ClearAll;
$DefaultFont = {"Times-Roman",10};
H[0,x_] = 1; H[1,x_] = 2 x; H[n_,x_]:= Simplify[2(x H[n-1,x] - (n-1) H[n-2,x])];
L[0,x_] = 1; L[1,x_] = 1 - x; L[n_,x_]:= Simplify[(2n-1-x)L[n-1,x] - (n-1)^2 L[n-2,x]];
P[0,x_] = 1; P[1,x_] = x; P[n_,x_]:= Simplify[((2n-1)x P[n-1,x] - (n-1) P[n-2,x])/n];
P[2,L[3,x]]
L[3,P[2,x]]