 An "n"-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree or less by a suitable choice of the nodes and weights for .Modern formulation using orthogonal polynomials was developed by Carl Gustav Jacobi 1826.The most common domain of integration for such a rule is taken as , so the rule is stated as

which is exact for polynomials of degree or less.