How do I generate the first four polynomials?

2013 5 10
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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.

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Friedrich
Friedrich 2013-5-10
编辑：Friedrich 2013-5-10

1 个投票

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

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