[math-fun] Simpson's rule and Gaussian Quadrature

It seems that the weights in Gaussian Quadrature over the interval [-1,+1] are proportional to sqrt(1 - x^2). This means that means the weights do not become constant inside the interval as the number of evaluation points increases. The weights must vary inversely with the density of roots of the Legendre polynomial. On the other hand, the weights vary smoothly, rather than jumping around as in Simpson's rule. -- Gene