ABSTRACT
Note that the weight function on the right-hand side is constant for all nodes in the summation. This formula can be made to be exact for all polynomials f(x) = xn for n = 0,1, .. . ,N. Setting up the necessary equations, and then solving them, we find that w = 2/N, and the {x~c} are the roots of the polynomial part of
where &i = N 11 ui du = { 0 N 2 -1 i + 1
for odd i , ~ . . The polynomial part, llN, tor even a.
