Computes the sample points and weights for Gauss-Legendre quadrature. These sample points and weights will correctly integrate polynomials of degree or less over the interval with the weight function .
deg : int
Number of sample points and weights. It must be >= 1.
x : ndarray
1-D ndarray containing the sample points.
y : ndarray
1-D ndarray containing the weights.
The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that
where is a constant independent of and is the k’th root of , and then scaling the results to get the right value when integrating 1.