 It can be shown (see Press, et al., or Stoer and Bulirsch) that the quadrature nodes are the roots of a polynomial belonging to a class of orthogonal polynomials (the class orthogonal with respect to a weighted inner-product).This is a key observation for computing Gauss quadrature nodes and weights.For the simplest integration problem stated above, i.e., is well-approximated by polynomials on formula_8, the associated orthogonal polynomials are Legendre polynomials, denoted by .