How to make this Lagrange formula vectorized work for all Ln? This is only for L3

if true
  % code
end

function f_handle = make_L3(x_in) x3 = x_in(3); not_x3 = [x_in(1:2), x_in(4:end)];

denominator_values = x3 - not_x3;
denominator = prod(denominator_values);

f_handle = @(x) (prod(x - not_x3) / denominator);
end

The input 3 represents the 3rd element in vector set to be plugged in. How do I modify this formula to give me all of Ln using the same vectorized procedure? Can I just tweak this code somehow?