Let {w} be a set of weights and {x)} a set of Gauss points, such that L where is satisfied for k = 0, 1, 2, ..., N = 2n - 1. Show that the weights must satisfy n x dx = w(n) f(x(n)) i=1 20 (") = [ L() (x) dx n L(n)(x) = II k=1 ki x - (n) k (n) - xk

Let {wi(n)} be a set of weights and {xi(n)} a set of Gauss points, such that 11xkdx=i=1nwi(n)f(xi(n)) is satisfied for k=0,1,2,,N=2n1. Show that the weights must satisfy wi(n)=11Li(n)(x)dx where Li(n)(x)=k=1k=inxi(n)xk(n)xxk(n)