 For integrating "f" over formula_2 with Gauss-Legendre quadrature, the associated orthogonal polynomials are Legendre polynomials, denoted by .With the -th polynomial normalized to be monic, i.e.so that , the -th Gauss node, , is the -th root of and the weights are given by the formula 

Some low-order quadrature rules are tabulated below for integrating over formula_4.