以勒让德多项式为基本函数,在区间[-1,1]上把f(x)=x^4+2x^3展开为广义傅里叶级数,求MATLAB程序

function f = Legendre(y,k,x0)
% 用勒让德多项式逼近已知函数
% 已知函数：y
% 逼近已知函数所需项数：k
% 逼近点的x坐标：x0
% 求得的勒让德逼近多项式或在x0处的逼近值f
syms t;
P(1:k+1) = t;
P(1) = 1;
P(2) = t;
c(1:k+1) = 0.0;
c(1)=int(subs(y,findsym(sym(y)),sym('t'))*P(1),t,-1,1)/2;
c(2)=int(subs(y,findsym(sym(y)),sym('t'))*P(2),t,-1,1)/2;
f = c(1)+c(2)*t;
for i=3:k+1
P(i) = ((2*i-3)*P(i-1)*t-(i-2)*P(i-2))/(i-1);
c(i) = int(subs(y,findsym(sym(y)),t)*P(i),t,-1,1)/2;
f = f + c(i)*P(i);
if(i==k+1)
if(nargin == 3)
f = subs(f,'t',x0);
else
f = vpa(f,6);
end
end
end
调用：syms x t;
f=x^4+2*x^3;
f = Legendre(f,3);
fourier(f,t)