function f = Gauss(x,y,x0)

if(length(x) == length(y))
    n = length(x);
else
    disp('x和y的維數不相等！');
    return;
end

xx =linspace(x(1),x(n),(x(2)-x(1)));
if(xx ~= x)
    disp('節點之間不是等距的！');
    return;
end

if( mod(n,2) ==1)
    if(nargin == 2)
        f = GStirling(x,y,n);
    else if(nargin == 3)
        f = GStirling(x,y,n,x0);
        end
    end
else
    if(nargin == 2)
        f = GBessel(x,y,n);
    else if(nargin == 3)
        f = GBessel(x,y,n,x0);
        end
    end
end

function f = GStirling(x,y,n,x0)
syms t;
nn = (n+1)/2;
f = y(nn);

for(i=1:n-1)
    for(j=i+1:n)
        y1(j) = y(j)-y(j-1);
    end
    if(mod(i,2)==1)
        c(i) = (y1((i+n)/2)+y1((i+n+2)/2))/2; 
    else
        c(i) = y1((i+n+1)/2)/2;
    end
    
   
    if(mod(i,2)==1) 
        l = t+(i-1)/2;
        for(k=1:i-1)
            l = l*(t+(i-1)/2-k);
        end
    else
        l_1 = t+i/2-1;
        l_2 = t+i/2;
        for(k=1:i-1)
            l_1 = l_1*(t+i/2-1-k);
            l_2 = l_2*(t+i/2-k);            
        end
        l = l_1 + l_2;
    end
    
    l = l/factorial(i);
    f = f + c(i)*l;
    simplify(f);
    f = vpa(f, 6);
    y = y1;
    
    if(i==n-1)
        if(nargin == 4)
            f = subs(f,'t',(x0-x(nn))/(x(2)-x(1)));
        end
    end
end

function f = GBessel(x,y,n,x0)
syms t;
nn = n/2;
f = (y(nn)+y(nn+1))/2;

for(i=1:n-1)
    for(j=i+1:n)
        y1(j) = y(j)-y(j-1);
    end
    if(mod(i,2)==1)
        c(i) = y1((i+n+1)/2)/2; 
    else
        c(i) = (y1((i+n)/2)+y1((i+n+2)/2))/2;
    end
    
   
    if(mod(i,2)==0) 
        l = t+i/2-1;
        for(k=1:i-1)
            l = l*(t+i/2-1-k);
        end
    else
        l_1 = t+(i-1)/2;
        l_2 = t+(i-1)/2-1;
        for(k=1:i-1)
            l_1 = l_1*(t+(i-1)/2-k);
            l_2 = l_2*(t+(i-1)/2-1-k);            
        end
        l = l_1 + l_2;
    end
    
    l = l/factorial(i);
    f = f + c(i)*l;
    simplify(f);
    f = vpa(f, 6);
    y = y1;
    
    if(i==n-1)
        if(nargin == 4)
            f = subs(f,'t',(x0-x(nn))/(x(2)-x(1)));
        end
    end
end