A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m + 1 points and fits all polynomials to degree 2m, so it effectively fits exactly all polynomials of degree 2m - 1. It uses a weighting function W(x) = 1 in which the endpoint -1 in the interval [-1, 1] is included in a total of n abscissas, giving r = n - 1 free abscissas. The general formula is integral_(-1)^1 f(x) d x = w_1 f(-1) + sum_(i = 2)^n w_i f(x_i). The free abscissas x_i for i = 2, ..., n are the roots of the polynomial (P_(n - 1)(x) + P_n(x))/(1 + x), where P(x) is a Legendre polynomial.

Chebyshev quadrature | Lobatto quadrature