How do I generate the first four polynomials?

A Legendre polynomial of degree n is given by the following expression: Pn(x)=1/(2^n*n!) * nth derivative of (x^2-1)^n

How do I generate the first four polynomials?

I have tried the following code but no output is being given:

function y=f(x,n)
function z=S(w,n)
for k=4
    syms w
    z=(w^2-1)^n
    subs(S,w,x)
    diff(S,n);
    y=(1/2^n)*factorial(n)*S
    subs(f,w,x)
end

Thanks in advance.

Answer 1

[Friedrich]

Hi,

what about:

for i=1:4
    P{i} = 1/(( 2^i)*factorial(i)) * diff(sym(['(x^2-1)^',num2str(i)]),i)
end

Since you have Symbolic MATH Toolbox you can also do:

for i=1:4
    L{i} = feval(symengine,'orthpoly::legendre',i,'x');
end